Question

Given an arithmetic sequence with a thirteenth term, a13 = −111, and a common difference, d = 11, find the 5th term: a5 = ?

Answer 1

a5 = -199

Explanation:

The formula to find the nth term in an arithmetic sequence is:

`a_(n)=a_(1)+(n-1)d`, where a1 is the first term, n is the term position (e.g. 5th, 13th), and d is the common difference.

To find a5, we at least need to find a1. We can plug in a13 (-111) for an and 13 for n:

`-111=a_(1)+(13-1)11\\ -111=a_(1)+12*11\\ -111=a_(1)+132\\ -243=a_(1)`

Since we now know a1, we can find find a5 (remembering to plug in 5 for n):

`a_(5)=-243+(5-1)11\\ a_(5)=-243+4*11\\ a_(5)=-243+44\\ a_(5)=-199`