Write the explicit formula for the geometric sequence represented by the recursive formula.
a1 = 4
an = 5 · an-1
a) an = 4 · 5n
b) an = 5 · 4n
c) an = 4 · 5n-1
d) an = 5 · 4n-1

Option C is correct.

Explanation:

Explicit formula for the geometric sequence is given by:

where r is the common ratio

Given the recursive formula for geometric sequence:

For n =2

⇒

For n =3

⇒

Common ratio(r):

⇒ r = 5

Therefore, the explicit formula for the geometric sequence represented by the recursive formula is:

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

step-by-step explanation: