Question

If the first term in a sequence is -18 and each term after the first is 4 times the preceding term. Which of the following explicit functions defines the sequence described above, where n is a positive integer?

A f(n) = -18(-4)
(B f(n) = -18(4)n-1
Cf(n)= (-18.4)"
D f(n) = (-18.4)n-1

Answer 1

`b_n=-18\cdot 4^(n-1)`

Explanation:

If the first term in a sequence is
`b_1=-18` and each term after the first is 4 times the preceding term, then the second term is

`b_2=b_1\cdot 4=-18\cdot 4,`

the third term is

`b_3=b_2\cdot 4=-18\cdot 4\cdot 4=-18\cdot 4^2,`

the fourth term is

`b_4=b_3\cdot 4=-18\cdot 4^2\cdot 4=-18\cdot 4^3,`

...

the nth term is

`b_n=b_(n-1)\cdot 4=...=b_1\cdot 4^(n-1)=-18\cdot 4^(n-1)`