Question

Consider a sequence given by the formula an = an−1 − 5, where a1 = 12 and n ≥ 2.

a. List the first five terms of the sequence

Answer 1

12, 7, 2, -3 & -8

Explanation:

The initial value given is 12 i.e.
`a_(1) = 12`

The initial assumption based on the given information is that the formula given is as follow

`a_(n) = a_((n-1)) -5`

To find the first five terms we need to find a1, a2, a3, a4 and a5

Since we have already been given the value of a1 i.e. 12

The remaining value are as follow

`a_(1) = 12\\ a_(2) = a_(1)  - 5 = 7\\ a_(3) = a_(2) -5 = 2\\ a_(4) = a_(3) - 5 = -3\\ a_(5)  = a_(4) - 5 = -8`