Question

Vera and fenyang were asked to find an explicit formula for the sequence 26,10, -6,-22… Vera said the formula is g(n) =26 - 16(n-1) Fenyang said the formula is g(n) =42 - 16n Which one of them is right?

Answer 1

Both

Explanation:

Answer 2

Both

EXPLANATION

The terms of the given sequence are:

`26,10,-6,-22,...`

The first term of this sequence is

`a_1=26`

The common difference is

`d = 10 - 26 = - 16`

The nth term of this sequence is;

`a_n=a_1+d(n-1)`

`g(n)=26 - 16(n-1)`

This is the same as Vera's formula,

If we expand, we get,

`g(n) = 26 - 16n + 16`

This simplifies to,

`g(n) = 42- 16n`

This Feynyang's formula