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

Answer:

$b_n=-18\cdot 4^{n-1}$

Step-by-step 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

$b_n=b_{n-1}\cdot 4=...=b_1\cdot 4^{n-1}=-18\cdot 4^{n-1}$