Introduction to sequence - Sequences & Series Video Lecture - Class 11

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introduction to sequence sequence is
nothing but an ordered list which has a
pattern to repeat sequence is nothing
but an ordered list which has a pattern
for example money in piggy bank so you
have this piggy bank ultra piggy bank
for you to give an which is at this
phone where you can put money and this
is the stand so this is the big bang I
will make a decoration smiley face this
is the pre bang this is a PvP key bank
where you do put money now let's suppose
I am talking about first of Jan so your
dad told ok let's start the gown on
first and since the new year will give
you hundred rupees and every alternating
or every every day every next day he
will give you 10 ability number second
Jan I give you 10 rupees on 3rd Jan
again he give it will replace it for
Chen also he gave you 10 rupees so daily
daily he keeps giving you 10 rupees now
at any point of time you want to know
how much money you have your piggy bank
then you can use sequence for example on
Jan the amount was 100 Jan first on Jan
second
it was hundred plus 10 that is 110 on
jab third it was 110 plus 10 that is 120
on Jan fourth is a 120 plus 10 that is
130 and Jan 5th it is 130 plus 10 140
similarly it will keep increasing so you
see is a pattern here 100 110 120 130
140 that's a pattern here the pattern is
that the difference between any two
consecutive number is 10
you see 110 - have it at this ten
hundred twenty - hundred ten ten hundred
thirty - one in twenty ten 140 - as a
13-10
so you see there is a pattern here
correct so such kind of ordered list
which has a pattern is called sequence
we have different kinds of sequence
we'll go through it but just understand
what a sequence sequence is nothing but
an ordered list the list is order it is
in the ascending order that is it
increasing just from small to big big
increasing it can also be decreasing the
list can also be from big to small but
this should be an ordered and should
have a pattern then it is called
sequence let's take one more example of
sequence for example on the month of
January she's Ford Mathis question every
day for math question every day
according now your teacher is telling
you that you keep increasing your counts
that every month you double that is in
the month of feb 4 and evident a math
question or a day in the month of March
he expects you to go for 8 into that is
16 questions math questions similarly
for Apple he expects you to again double
it 16 to 242 so if you see there is a
pattern here for a 16 32 this becomes 64
keep going there is a pattern that each
number is double whose number 4 into 2
is 8 8 into 2 is 16 16 into 2 with 32 32
into 2 is 64 that means there is a
pattern here all the numbers I in the
other ordered list is an increasing
order and there is a pattern the pattern
is the N X term and n plus 1 of the term
should have some relation so this is
relation here so this is a pattern any
kind of pattern is called sequence the
pattern should be ordered list will go
through this in details just understand
what a secret
sequence is nothing but an ordered list
which has a pattern so we define
sequence tom sequence is an ordered list
of object as we explained in the
scenarios ever that money in the piggy
bank or if you ask double the number of
questions
those things are pattern so
mathematically sequence is nothing but
an ordered list of God for example we
have seen in money bank it was hundred
in K 110 it became 120 130 140 this was
the total amount in the piggy bank or in
case of maths question you were asked to
solve core questions in eight questions
and seen potion correcting potions then
64 questions and 128 questions the list
keeps increasing every month so you see
there is a pattern here in first case
the diff is constant and that is 10 and
here not a difference but the division
here the division because this by this
or this by this despite this a dealer is
constant and that is 2 so in both the
case both are ordered list and Buddha
having a pattern let's take my example
we have to write five elements of the
sequence where T n is going to put n
plus 3 so now what we'll do you will
first say and is going to 1 so n is
going to 1 what we get T 1 is equal to 2
into 1 plus 3 that is nothing but Y
similarly T 2 is equal to 2 into n is
going to 2 here we put 2 plus 3 that is
2 into 2 4 plus 3 7 similarly T 3 is
equal to 2 into n and his 3 in this case
plus 3 that is 9 similarly T 4 is
nothing but 2 into 4 plus 3 and is 8
plus 3 11 and D 5 is nothing but 2 into
5 plus 3 that is 30 thus we can say that
first
Tom's first five terms of when plus 1
this is the N plus 3 30 as dumb is equal
to 5 7 9 11 40
similarly let's take for example so we
have to find for Tian has got 2 n square
per spec here also what we'll do we'll
then put the value of 1 n is equal to 1
T 1 is going to 1 square this is equal
to 1 T 2 is equal to 2 squared is equal
to 4 e 3 is equal to 3 square is equal
to 9 T 4 is equal to 4 square is equal
to 16 and D 5 is going to do 5 square
that is 25 so what we have got now I
will write first 5 terms is equal to
sorry this is not 1 this is 1 4 9 16 and
25 similarly take some take let's take
for example TN is going to end you here
also will do the same thing
so here we'll say well let him t1 is
going to 1 cube that is 1 T 2 is equal
to 2 Q that is 8 t 3 is equal to 3 Q
that is 27 T 4 is equal to 4 Q that is
64 and T 5 is equal to 5 u that is 125
so if you see the series what we get is
the 5 terms it is equal to nothing but 1
8 27 64 and 125
this is our answer so what we have done
here we know in the NL term we have put
the value of n is equal to one two three
and four or five to get T 1 T 2 T 3 T 4
to 5 and thus that is the answer let's
take an example here we have to find the
end of term so we are asked to find 15
term of this sequence en is equal to n
minus 2 n minus 3 and plus 5 so we have
been told that a M is equal to n minus 2
into n minus 3 into n plus 5 so we have
to find find a 15 just we will replace n
the 15 so the placing my 15 we get 15
minus 2 this is 15 my n minus 3 is 1 15
minus 3 and this become 15 plus 5 so
this becomes 15 minus 2 is 30 15 minus 3
is 12 into 15 plus 5 is equal to 20 so
what we get is this is nothing but 30
into 2 is equal to 156 into 20 and this
is nothing but 3 1 2 0 and this is our
answer
very simple we have to find 50 in term
we have been given the equation of a n
just replace n with 50 and you get the
answer we will now see sequence types
based on number of items so we have B's
or number items we have finite and
infinite signals if we say that the
sequence is finite that means it has
definite number of elements example I
say that their sequence which is 2 4 6 8
10 12 this is the sequence and starts
with 2 ends with 12 and the difference
is always 2 so it is a sequence and the
number of items is 1 2 3 4 5 6 so there
are 6 and items so it is finite another
case let's suppose the same sequence or
let's suppose we have sequence 1
two three four five six co-hosted
infinity so in that case the number of
element in this sequence is infinite so
this is infiniteness it's pretty simple
sequence which has finite number of
elements is called finite sequence and
sequence which has infinite number of
element is called infinite sequence
let's learn the sequence based on the
pattern types we have automatic defense
geometric sequence and Fibonacci
sequence so based on pattern types we
have three types of sequence arithmetic
sequence geometric sequence and Fiona
key signals so first let me touch upon
all these in case of automatic sequence
the difference is constant the
difference is going to be constant so
that means a n plus 1 element minus a
and you take any least any element for
this
the difference is constant in case of
geometric sequence the division is
constant division this constant that
this you say any a n plus element and we
divide by a n you get some constant
number say K 1 K 2 so that you don't get
confused both are different values and
what are constant for female icky series
what happens is T of n plus 2 is equal
to T or T of n plus 2 your n plus so
every third number is somehow first 2 or
the preceding two numbers adding
examples of all these three in case of
earth Matic sequence for example we had
a piggy bank thing where the odd number
the value was 100 110 rupees 120 rupees
130 rupees these were the value of money
in the piggy bank on each passing day so
here if you see the difference is
constant the difference here is 10 the
difference here is 10 the difference
here is 10 here of the references 10
heroes on it instead the such kinds of
sequence is called automatic sequence we
also call it a B in case of GP let us
take the example of the number of
questions
by the student in first month he was
supposed to solve phone questions per
month average in second month eight
question in third one sixteen question
in fourth month 32 potions in next month
was 64 question still scary song so if
you see here 8 by 4 is equal to 2 16 by
8 is going to do 6 32 by 6 is equal to
64 by 32 color tools so if you see here
the division is constant you take any
number and you divide that number by the
pressing number then division is
constant so this type of sequence is
called genie
now let's the example of aminika series
so if we have 0 and then 1 0 plus 1 is
equal to 1 1 plus 1 is equal to 2 1 plus
2 is equal to 3 3 plus 2 is equal to 5 5
plus 3 is equal to 8 8 plus 5 is equal
to 14 13 plus 8 is equal to 21 21 plus
30 is going to 34 34 plus 21 is equal to
15 fine you keep engaging this you can
make this 9 and 89 so this kind of
sequence is called
Fibonacci series thank you visit exam
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