How do you write an explicit formula for the general term of the sequence [-4,2,8,14,...]?

Kaylynn Cook

Kaylynn Cook

Answered question

2022-11-11

How do you write an explicit formula for the general term of the sequence [-4,2,8,14,...]?

Answer & Explanation

Lillianna Salazar

Lillianna Salazar

Beginner2022-11-12Added 22 answers

This looks like an arithmetic sequence, so we start by finding the common difference d.
d = a n a n - 1
Your sequence is [−4,2,8,14,…].
For a 2 , d = a 2 - a 1 = 2 ( - 4 ) = 2 + 4 = 6
For a 3 , d = a 3 - a 2 = 8 - 2 = 6
For a 4 , d = a 4 - a 3 = 14 - 8 = 6
So d = 6
The general formula for an arithmetic sequence is
a n = a 1 + ( n - 1 ) d
So, for your sequence, the general formula is
a n = - 4 + 6 ( n - 1 ) = - 4 + 6 n - 6
a n = 6 n - 10

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