Question

G(1) = -29
g(n) = g(n-1).(-4)
Find an explicit formula for g(n).
g(n) =

Answer 1

an = -29(-4)^(n-1).

Explanation:

There is a common ratio (r) of -4 so it is a geometric sequence.

The first term a1 = -29.

an = a1 r^(n-1)

an = -29(-4)^(n-1) is the explicit formula.

Answer 2

g(n) = - 29
`(-4)^(n-1)`

Explanation:

Given the recursive formula

g(n) = g(n - 1). - 4

This tells us that to obtain a term in the sequence we multiply the previous term by - 4.

We are dealing with a geometric sequence with explicit formula

g(n) = g(1)
`(r)^(n-1)`

Here g(1) = - 29 and r = - 4, thus

g(n) = - 29
`(-4)^(n-1)` ← explicit formula