Class 11 Exam > Class 11 Videos > Example GP Geometric Progression-1 (Part - 13)- Sequences and Series, Mathematics, Class 11
Example GP Geometric Progression-1 (Part - 13)- Sequences and Series, Mathematics, Class 11 Video Lecture
FAQs on Example GP Geometric Progression-1 (Part - 13)- Sequences and Series, Mathematics, Class 11 Video Lecture
| 1. What is a geometric progression (GP)? |  |
Ans. A geometric progression (GP) is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the GP 2, 4, 8, 16, the common ratio is 2, as each term is obtained by multiplying the previous term by 2.
| 2. How can I find the nth term of a geometric progression? | |
Ans. To find the nth term of a geometric progression (GP), you can use the formula: nth term = a * r^(n-1), where "a" is the first term and "r" is the common ratio. For example, in the GP 3, 6, 12, 24, to find the 5th term, you would use the formula: 5th term = 3 * 2^(5-1) = 3 * 2^4 = 48.
| 3. What is the sum of a finite geometric progression? | |
Ans. The sum of a finite geometric progression (GP) can be calculated using the formula: sum = a * (1 - r^n) / (1 - r), where "a" is the first term, "r" is the common ratio, and "n" is the number of terms. For example, in the GP 1, 2, 4, 8, if you want to find the sum of the first 4 terms, you would use the formula: sum = 1 * (1 - 2^4) / (1 - 2) = 1 * (1 - 16) / (1 - 2) = -15.
| 4. How can I determine if a sequence is a geometric progression? | |
Ans. To determine if a sequence is a geometric progression (GP), you need to check if there is a common ratio between consecutive terms. You can do this by dividing each term by its previous term. If the result is always the same, then the sequence is a geometric progression. For example, in the sequence 3, 6, 12, 24, dividing each term by its previous term gives the common ratio of 2.
| 5. Can a geometric progression have a common ratio less than 1? | |
Ans. Yes, a geometric progression (GP) can have a common ratio less than 1. In such cases, the terms of the GP will decrease in value as the index increases. For example, in the GP 4, 2, 1, 0.5, the common ratio is 0.5, and each term is obtained by dividing the previous term by 2.
Text Transcript from Video
hello friends this video sequence and
series part 13 is brought to you by exam
fear calm
no more fear from exam before watching
this video please make sure that you
have watched video part 1 - Part A
example we are told add someone first
three terms of GPA is 13 by 12 and their
product is minus 1 you have to find
common ratio and so if you have to take
three terms in GP will take a by our a
and here here we see the ratio of total
is God and we know that if you multiply
all this thing are you get cancelled
immediately so it's always good to take
terms in this form a by our DNA if
you're asked big three terms so we take
the symptoms as they are and yeah we are
told that somehow first three terms is
13 by 12 that is a by r plus a plus AR
which is 13 by 9 is the first equation
also we had told that product of these
term is 1 that is e by r into e into
minus 1 RR cancel so that means a q is
equal to minus 1 so E is equal to minus
1 so we have found a below it now we'll
put this value of a this equation first
so you get minus 1 my R minus 1 minus R
is equal to 13 by 12 we just put a is
better - for me so I will solve this it
will take this both this side r plus 1
by r is equal to minus 1 minus 13 by
then that is nothing but it's 2l minus
25 by 2 30 by 2 or 3-bedroom 3-bath -
that's what we get or R square plus 1 by
r is equal to
- 2500 I will multiply this two so we
get 12 R squared plus 2 n plus 25 is
producing or when R square plus 25 odd
less sequencing we have this equation
now we can say that this is nothing but
12 R square plus 16 odd plus minus 12 is
equal to 0 in s factorizing this
equation so this becomes 12 hours 16 are
for common so for our into 3r plus o and
here we get 3 is equal to 3 R so R is
equal to minus 3 by 4 or - so we have
got these together - V by 4 n - buh-bye
that's the answer so E is equal to 1
minus 1 common term wave form sorry
terms first comes wave form and we have
to find the dish we have to find that
terms also so we have a 's equal to this
and R is equal to minus 3 this is the
term we have formed hello
now what we'll do we'll first as you -
go to - 3 by 3 so the terms are a by odd
a and area so when we assume R is equal
to minus C by 4 so a my R will become o
by 3 this minus 1 divided by minus 3 by
4
he said become minus 1 this will become
minus 1 into minus 3 so the terms are 4
by 3 1 minus 1 and this is 1 set the
second set we resume our is equal to
minus 4 by 3 so that term will be minus
1 by minus 4 by 3 minus 1 n minus 1 into
minus 4/5 so what we'll get here we get
3 by 4 minus 1 and so we have two sets
set 1 in
we reduced assets they are the terms to
set of terms common ratio is - mmm -
fall back
this is that
this is little tricky example here we
have to find some of 777 7 7 7 4 times 7
2 n terms if you observe this there is a
pattern here this is 1 times 7 this is 2
times this is 3 times this is 4 times it
keeps going for such kind of patterns
what we do is we divide and multiply by
9 in this case we'll say you can write
the same thing in this form 7 by 9 into
1 sorry
999 10 times the same pattern when I
took 7 by 9 common I got this nein nein
nein nein nein nein nein nein nein why I
did this because this - ball - 10 - 1
this is equal to 99 is going to 10
square minus 1 999 is go to 10 cube
minus 1 and 9900 is go to 10 4 minus 1
so we have this is a question where both
a PNG are they're both a PNG such kind
of pushes when you go to example 5 comma
5 5 5 5 5 5 5 5 5
she such kind of questions you have to
first divide and multiply 9 so we got
this if I'm going for some some of
series SN that is nothing but 7 my mind
and a common 9 + 99 + 9 9 9 plus 9 9 9 9
till n terms this is the song also as I
have told the reason why we have written
this in this form is because 9 we can
write as 10 minus 1 similarly 99 again
set and square minus 1 and 9 99 is
I can say is 10 Q minus 1 plus 10 Q is
1000 minus 1 is this suddenly 9 thousand
999 against a 10 4 minus 1 it keeps
going to end um so if you see this is
the N is equal to 1 and it's going to 2x
will be 3 and 2 to 4 so NS term I can
say is nothing but 10 to the power n
minus 1 because this is a pattern here
10 to the power 1 minus 1/10 word 2-1 in
the power 3 minus 1 into power 4 minus 1
till 10 to the power n minus 1 so we can
now also write this in this form 7 by 9
into 10 plus 10 square letters and Q
plus 10 to the power 4 dot-dot-dot 10 to
the power n minus 7 by 9 into 1 plus 1
plus 1 plus 1 and now this is the Jeep
this is a GP where a is equal to L right
a is equal to 10 are the also called of
10 because 10 square by 10 is 10 10 cube
by 10 square is again 10 where a not
both are tennis this will nothing be we
can write this as a that is 10 into R to
the power n minus 1 that is 10 to the
power n minus 1 by r minus 1 that is n
minus 1 the second part we can write
this is nothing but 7 by 9 into 1 plus 1
plus 1 till n that becomes n because if
you add 1 n times that becomes n o will
take seven men in common
this will be 10 by 9
because 10 minus 1 9 into 10 to the
power n minus 1 - and because we have to
get sin man in common and that is our
ends so what we have done please note
whenever you have sequence in this form
example 3 3 comma 3 3 comma 3 3 3 comma
3 3 3 3 such equations you can write in
this form cut by 9 into nine ninety nine
nine nine nine nine nine nine nine in
this form why we have done this because
nine we can say is good to 10-1 99
against 8 n square minus 1 9 99 I can
say thank you - 119 thousand 999 against
a 10 4 minus 1 10 to the power of 4
minus 1 thus will get a GP out of this
please no such kind of questions come in
exams understand the pattern if you get
such questions where you have example 2
222 tipple - 4 x 2 dot dot dot n times
if you want to find some of this then
you can say this adds 2 by 9 into nine
ninety nine nine nine nine nine nine
nine nine ten times because nine we can
say ten minus one ninety nine I can say
ten square minus one this I can say ten
to minus one this I can say ten for - oh
that's for the socks pushes please make
an box pattern thank you visit exam
viacom to watch free educational videos
try free online tests in the best
quality study materials study from the
best tutors and mentors and much more
thanks again
series part 13 is brought to you by exam
fear calm
no more fear from exam before watching
this video please make sure that you
have watched video part 1 - Part A
example we are told add someone first
three terms of GPA is 13 by 12 and their
product is minus 1 you have to find
common ratio and so if you have to take
three terms in GP will take a by our a
and here here we see the ratio of total
is God and we know that if you multiply
all this thing are you get cancelled
immediately so it's always good to take
terms in this form a by our DNA if
you're asked big three terms so we take
the symptoms as they are and yeah we are
told that somehow first three terms is
13 by 12 that is a by r plus a plus AR
which is 13 by 9 is the first equation
also we had told that product of these
term is 1 that is e by r into e into
minus 1 RR cancel so that means a q is
equal to minus 1 so E is equal to minus
1 so we have found a below it now we'll
put this value of a this equation first
so you get minus 1 my R minus 1 minus R
is equal to 13 by 12 we just put a is
better - for me so I will solve this it
will take this both this side r plus 1
by r is equal to minus 1 minus 13 by
then that is nothing but it's 2l minus
25 by 2 30 by 2 or 3-bedroom 3-bath -
that's what we get or R square plus 1 by
r is equal to
- 2500 I will multiply this two so we
get 12 R squared plus 2 n plus 25 is
producing or when R square plus 25 odd
less sequencing we have this equation
now we can say that this is nothing but
12 R square plus 16 odd plus minus 12 is
equal to 0 in s factorizing this
equation so this becomes 12 hours 16 are
for common so for our into 3r plus o and
here we get 3 is equal to 3 R so R is
equal to minus 3 by 4 or - so we have
got these together - V by 4 n - buh-bye
that's the answer so E is equal to 1
minus 1 common term wave form sorry
terms first comes wave form and we have
to find the dish we have to find that
terms also so we have a 's equal to this
and R is equal to minus 3 this is the
term we have formed hello
now what we'll do we'll first as you -
go to - 3 by 3 so the terms are a by odd
a and area so when we assume R is equal
to minus C by 4 so a my R will become o
by 3 this minus 1 divided by minus 3 by
4
he said become minus 1 this will become
minus 1 into minus 3 so the terms are 4
by 3 1 minus 1 and this is 1 set the
second set we resume our is equal to
minus 4 by 3 so that term will be minus
1 by minus 4 by 3 minus 1 n minus 1 into
minus 4/5 so what we'll get here we get
3 by 4 minus 1 and so we have two sets
set 1 in
we reduced assets they are the terms to
set of terms common ratio is - mmm -
fall back
this is that
this is little tricky example here we
have to find some of 777 7 7 7 4 times 7
2 n terms if you observe this there is a
pattern here this is 1 times 7 this is 2
times this is 3 times this is 4 times it
keeps going for such kind of patterns
what we do is we divide and multiply by
9 in this case we'll say you can write
the same thing in this form 7 by 9 into
1 sorry
999 10 times the same pattern when I
took 7 by 9 common I got this nein nein
nein nein nein nein nein nein nein why I
did this because this - ball - 10 - 1
this is equal to 99 is going to 10
square minus 1 999 is go to 10 cube
minus 1 and 9900 is go to 10 4 minus 1
so we have this is a question where both
a PNG are they're both a PNG such kind
of pushes when you go to example 5 comma
5 5 5 5 5 5 5 5 5
she such kind of questions you have to
first divide and multiply 9 so we got
this if I'm going for some some of
series SN that is nothing but 7 my mind
and a common 9 + 99 + 9 9 9 plus 9 9 9 9
till n terms this is the song also as I
have told the reason why we have written
this in this form is because 9 we can
write as 10 minus 1 similarly 99 again
set and square minus 1 and 9 99 is
I can say is 10 Q minus 1 plus 10 Q is
1000 minus 1 is this suddenly 9 thousand
999 against a 10 4 minus 1 it keeps
going to end um so if you see this is
the N is equal to 1 and it's going to 2x
will be 3 and 2 to 4 so NS term I can
say is nothing but 10 to the power n
minus 1 because this is a pattern here
10 to the power 1 minus 1/10 word 2-1 in
the power 3 minus 1 into power 4 minus 1
till 10 to the power n minus 1 so we can
now also write this in this form 7 by 9
into 10 plus 10 square letters and Q
plus 10 to the power 4 dot-dot-dot 10 to
the power n minus 7 by 9 into 1 plus 1
plus 1 plus 1 and now this is the Jeep
this is a GP where a is equal to L right
a is equal to 10 are the also called of
10 because 10 square by 10 is 10 10 cube
by 10 square is again 10 where a not
both are tennis this will nothing be we
can write this as a that is 10 into R to
the power n minus 1 that is 10 to the
power n minus 1 by r minus 1 that is n
minus 1 the second part we can write
this is nothing but 7 by 9 into 1 plus 1
plus 1 till n that becomes n because if
you add 1 n times that becomes n o will
take seven men in common
this will be 10 by 9
because 10 minus 1 9 into 10 to the
power n minus 1 - and because we have to
get sin man in common and that is our
ends so what we have done please note
whenever you have sequence in this form
example 3 3 comma 3 3 comma 3 3 3 comma
3 3 3 3 such equations you can write in
this form cut by 9 into nine ninety nine
nine nine nine nine nine nine nine in
this form why we have done this because
nine we can say is good to 10-1 99
against 8 n square minus 1 9 99 I can
say thank you - 119 thousand 999 against
a 10 4 minus 1 10 to the power of 4
minus 1 thus will get a GP out of this
please no such kind of questions come in
exams understand the pattern if you get
such questions where you have example 2
222 tipple - 4 x 2 dot dot dot n times
if you want to find some of this then
you can say this adds 2 by 9 into nine
ninety nine nine nine nine nine nine
nine nine ten times because nine we can
say ten minus one ninety nine I can say
ten square minus one this I can say ten
to minus one this I can say ten for - oh
that's for the socks pushes please make
an box pattern thank you visit exam
viacom to watch free educational videos
try free online tests in the best
quality study materials study from the
best tutors and mentors and much more
thanks again
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About this Video
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Nov 09, 2024 Last updated |
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