Question

A1=7 and an=an-1-4 find value of a6

Answer 1

a₆ = -13

Explanation:

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence. Therefore, when giving a recursive rule, we need to define the first term of the sequence, as it is not part of the formula.

Given recursive rule:

`\begin{cases}a_1=7\\a_n=a_(n-1)-4\end{cases}`

To find the value of a₆, use the recursive formula to find the first 6 terms of the sequence:

`a_1=7`

`a_2=a_1-4=7-4=3`

`a_3=a_2-4=3-4=-1`

`a_4=a_3-4=-1-4=-5`

`a_5=a_4-4=-5-4=-9`

`a_6=a_5-4=-9-4=-13`

Therefore, the value of a₆ is -13.