Question

Which is the 25th term of the arithmetic sequence where a1 = 7 and a9 = 71 ?
An explanation would be great!:)

Answer 1

the first step would be to find the common difference.

you are familiar with the formula \[\Large a_n = a_1 + (n-1)d\]yes?

Answer 2

a25=7+(24)d? whats d?

Answer 3

that's what we're going to find

Answer 4

first let us focus on a1 and a9

Answer 5

we say that a_n is the last term right? so if i make a_9 my a_n then it would become \[\Large a_9 = a_1 + (9-1)d\]
do you agree?

Answer 6

Yes, would we also plug in a1?

Answer 7

yup. and a9 too \[\Large \implies 71 = 7 + (9-1)d\]
do you think you can solve for d now?

Answer 8

56:)

Answer 9

how did you get 56 again?

Answer 10

My bad, 8..

Answer 11

So 199:)

Answer 12

yup that's what i got too