Question

F(5)= 12 for geometric sequence that is defined recursively by the formula f(n) = 0.3* f(n-1), where n is an integer and n is greater than 0. Find f(7). Round your answer by the nearest hundredth

Answer 1

The value of f(7) is 1.08

Solution:

Given that,

$f(5) = 12$

The sequence is defined recursively by formula:

$f(n) = 0.3 \times f(n-1)$

where n is an integer and n is greater than 0

Substitute n = 6 in given formula,

$f(6) = 0.3 \times f(6-1)\\\\f(6) = 0.3 \times f(5)\\\\Substitute\ f(5) = 12\\\\f(6) = 0.3 \times 12\\\\f(6) = 3.6$

Find f(7)

Substitute f = 7 in given formula

$f(7) = 0.3 \times f(7-1)\\\\f(7) = 0.3 \times f(6)\\\\f(7) = 0.3 \times 3.6\\\\f(7) = 1.08$

Thus the value of f(7) is 1.08