General Term & AP - - Arithmetic Progressions (AP) Video Lecture - Class 10

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will form of AP this is another form
this is a a plus da plus 2b plus degree
daughter why because we had told that D
is the common difference correct
and we also told that how a piece form
you take the first number on first
number you add the common difference
this becomes needless D on second number
you on this number you add again gamma
difference it is a plus B plus D now on
this number you again add common
difference that becomes a plus D plus D
on this number again you add common
difference that becomes a plus D plus D
plus D so you see this this is nothing
but a a plus D a plus 2 D a plus 3 D 8
plus 4 D this fashion right if you see
this this is nothing but a a Plus D V
Plus D V Plus V da nice OD for this is a
general form of you remember this
whenever you are asked to write a JP a B
and most of the questions can assume the
AP to be a a plus da plus 2 D plus 2 D
that so this is the general form of AP
by definition also only every time you
add a common difference for here also on
a we have I don't need this become e
plus D now on this term we add again D
this becomes wisdom on this term again
we added D this becomes a plus D plus D
plus d again on this term we added D
this becomes a plus four now let's talk
about finite and infinite DP AP which
has the last term is called finally + AP
which does not have a last step is
called infinity for example if I am
talking about AP let suppose three
common differences let suppose 5 2 3 + 2
5 5 + 2 7 7 + 2 9 9 plus 2 11 11
question degree and 13 is the large
number let's
so in this case we know they are finite
number of elements in the a B and this
has a last one this is called finite an
AP that does not have finite last term
is called infinitely for example let's
take one a B where the first term is
let's suppose for and the common
difference is three the next term will
be 4 plus 3 right and the next term will
be 4 plus 3 plus 3 correct and again the
next term will be 4 plus 3 plus 3 plus 3
M it is adding 3 in the previous terms
right so this term will be this you say
infinity be there is no end so it is
having dots in the end so the a B is
nothing but 4 7 7 3 10 + 3 13 holding
360 and dot dot dot so if you see in
this AP there is no last term there is
no last term because it is infinitely be
there is no last term correct so ap are
of two types finitely be an infinity be
a P which has the last term is called
finite EP P which does not have a last
term is called infinitely for example if
you see in real life scenario also let's
suppose the same girl Geeta Geeta is
putting money in the piggy bank
right the book is the piggy bank and
she's putting money in the piggy bank
now if she is telling that she will put
money only for one month right if she is
putting money only for one month showing
that is it is a finite AP because if you
see the series it will be 10 20 30 it
will somewhere stop after one month one
month maybe let's suppose 300 it is
somewhere it stop after one month so
this would be fine ideally but the same
Keith I said seaters that I will
continue doing it till my lifelong right
then there is no end the money will keep
going so in that case that will be
infinite correct finite ap is the one
which has an endpoint which has a
infinity P is the one which does not
have a pasta let us take some scenario
and tell us which neither this is a PMR
now the question says that the taxi fare
after each kilometer when the fare is 15
degrees for the first kilometer and
eight-piece for the additional middle so
for the first kilometer this guy is
charging 15 y 15 rupees and for the next
kilometres 8 rupees per kilometer so
let's find out first kilometer is
nothing but 15 rupees right and first
and second limit if you add or again say
that no new like if I'm hiring for 1
kilometer I had to pay 15 rupees why
because the taxi says 15 rupees for the
first kilometer if I'm hiring for 2
kilometer how much I have to pay 15 plus
8 15 by the first kilometer and 8 for
the second elevator correct if I'm
hiring for 3 kilometer how much I have
to pay 15 for the first kilometer and to
interview for the next 2 kilometres
because for any additional each limit
when he's chanting age would be if I am
having for 4 kilometres I have to be a
first kilometer and 3 into 8 for next 3
kilometres if I am having for 5
kilometers I have to be 15 to the first
kilometres and 4 into 8 for the next
kilometers
similarly if I'm hiring for six
millimeter I have to pay 15 for the
first climber term and fire beats per
kilometer for the next limiters
similarly for 7 kilometer I have to pay
shifting for the first kilometer and 6
bits for the next millimeter so you see
this this is nothing but 15 this is
nothing but 15 a 23 this is nothing but
16 plus 15 that is 31 this is nothing
bird 31 839 this is nothing but
for this Simon this is nothing worth 55
something 162 right now if you see this
if you see this you can write this term
in this fashion 1523 31
49:47
55 and 63 let's find the common
difference the common difference here is
a 32 - so in this 31 35 - 23 is also a
39 - 31 is also 847 - 39 is also a 55-47
is also 8 and 63 - it to the author if
you see here the common difference is
constant thus I can say that this isn't
easy where is it but what we have done
for 1 kilometer for 2 kilometer 3 4 5 6
7 kilometers I found a total cost that I
have to pay and I have arranged this
then I found that this is an EP because
the common difference is let's take one
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