Question

The first term of a sequence is -87. Each successive term is created by adding 7 to its previous term. The number 165 is which numbered term in the sequence?

Answer 1

Explanation:

The 36th sequence

Answer 2

The first term of a sequence is -87. 165 is 37th term of given Arithmetic sequence.

Solution:

Given that ;

First term of the sequence
`a_(1) = -87`

Also each successive term is created by adding 7 to its previous term. This means given sequence is an arithmetic sequence with common difference d = 7.

Let’s say 165 be
`n^(th)` term of above arithmetic sequence that is
`a_(n)` = 165. We need to determine n.

Formula of
`n^(th)` term of arithmetic sequence is as follows:

`\mathrm{a}_{\mathrm{n}}=\mathrm{a}_(1)+(\mathrm{n}-1) \mathrm{d}`

where
`a_(1)` is the first term of the sequence

"d" is the common difference ratio

Substituting the given values we get

165 = -87 + (n-1) 7

165 + 87 = 7n – 7

7n = 165 + 87 + 7

n =
`(259)/(7)` = 37

Hence 165 is 37th term of given Arithmetic sequence.