Question

What is the 32nd term of the arithmetic sequence where a1 = 13 and a13 = –59?

Answer 1

hi guyz

Answer 2

okay so we know nth term of an AP is a1 + (n-1)d .. here d is the common difference between each term.

so, a1=13.... (i)
a1 + (13-1)d=-59 ...(ii)

Put value of a1 from (i) in (ii) to solve it and get 'd'

then find 32nd term by the formula for any nth term!!


post what you get and verify, or if you face any problems!

Answer 3

@kmila03 Can you follow apoorvk's instruction?

Answer 4

mmhm not really im trying ...

Answer 5

a_13 = a_1 + 12d
Do you know this formula by now?

Answer 6

actually thats the problem i never seen this before

Answer 7

Memorize this formula, right now just plug number in!

Answer 8

ok, but what is 12d?

Answer 9

d is what we're looking for d = ...

Answer 10

d is the variable.. the common difference any two successive terms of an AP that you gotta find!

Answer 11

12d = a_13 - a_1
=>d = (a_13 - a_1) / 12
Can you plug in the numbers now?

Answer 12

so, can you guys do it. so ill see the steps?

Answer 13

okay i am continuing from my first post above..... just tell me do you understand linear equations?? did you understand the equations i wrote? and do you understand the question?

Answer 14

yes... so if i plug in the number from =>d = (a_13 - a_1) / 12
is = d=-6 ?

Answer 15

that's it kmila!!!!! you got it!!! what was there to be afraid of?? :)


now can you find the 32nd term??

Answer 16

thanks :)..... but how can i find 32nd?

Answer 17

okay any nth term "Tn" of an AP is
Tn=a + (n-1)d

where 'a' is the first term and 'd' is the common diff.
so, n is 32 here, first term is given and you just found out d.
plug in the values and get the answer!

Answer 18

it may so happen in future questions that the first term may not be given straightaway, but any two terms say 4th and 6th are provided, in that case you need to form 2 linear equations in 'a' and 'd' and solve to find 'a' and 'd'. then proceed with what the question asks!

Answer 19

so it will be -173?

Answer 20

Yeehhh, you got it :D

Answer 21

Riiighttttt-O!!!!!!! there you are!!

Answer 22

ok, thank u guys so much!!!

Answer 23

We hope you learn the formula AND keep PRACTICE :)