Find the 32nd term of the arithmetic sequence where a_1=15 and a_13=–57

Valery Cook

Valery Cook

Answered question

2022-10-16

Find the 32nd term of the arithmetic sequence where a 1 = 15 and a 13 = 57

Answer & Explanation

Jaylin Wheeler

Jaylin Wheeler

Beginner2022-10-17Added 11 answers

The general formula for a term of an arithmetic sequence is:
a n = a + d ( n - 1 )
where a is the initial term and d the common difference.
So:
- 72 = - 57 - 15 = a 13 - a 1 = ( a + 12 d ) - ( a + 0 d ) = 12 d
Hence:
d = - 6
a = a 1 = 15
So:
a 32 = a + 31 d = 15 - 6 31 = - 171

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