Question

-10, -14,18,-22 what's the explicit formula that can be used to determine the 9th term in this sequence A. A(n)=-4n-6 C. A(n)=n-10 B. A(n)=-4n-14. D. A(n)= n-4

Answer 1

`A(n) = -4n -10`

Explanation:

Given

`Sequence:\ -10, -14, -18, -22`

Required

Determine the formula for the nth term

The sequence shows arithmetic progression.

So, we need to determine the common difference (d) first

`d = A_2 - A_1`

In this case:

`A_2 = 2nd\ Term = -14`

`A_1 = 1st\ Term = -10`

So:

`d = -14 - (-10)`

`d = -14 + 10`

`d = -4`

The nth term is then calculated as thus:

`A(n) = A_1 + (n - 1)d`

`A(n) = -14 + (n - 1)* -4`

`A(n) = -14 -4n + 4`

`A(n) = -4n + 4-14`

`A(n) = -4n -10`