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C1 last term in an arithemetic sequence

Hello, I stumbled across a question that asks to prove the sum of the first n term of the series. But I got stuck in the first part. I don't get why the last term ofnthe sequence is expressed as a+(n-1)d and the second to last is a+(n-2)d. Thank you

Reply 1

S.G.

Think about what n actually means

Reply 2

coconut64

Original post by SGHD26716

Think about what n actually means

A certain term. So n =1 is the first nth term but why is it minus 2 for the second to last term?

Reply 3

KaylaB

Original post by coconut64

A certain term. So n =1 is the first nth term but why is it minus 2 for the second to last term?

So if a+(n-1)d is the last term, if we think we want the term before, we want to -1 to what the difference is multiplied by to get the term before.

For example if a=2 d=5 (meaning that each time 5 is added) and let's say that there's 10 terms in this sequence.
To find the last term we'd do 2+(10-1)5= 2+45 = 47
So to find the term before that we'd want to find the 9th term we'd do
2+(9-1)5 = 2+40 = 42
n=9 because we want to find the 9th term

So for a sequence with n terms, to find the last term we'd multiply the difference by (n-1)
If we want to find the second to last term, we want to find the (n-1)th term, so again we -1 from that so we have to multiply the difference by (n-2)