Question

Complete the recursive formula of the geometric sequence − 0.6   ,   3   , − 15   ,   75 , . . .

Answer 1

$a_n = -0.6 \times (-5)^{n - 1}$ is the recursive formula of the geometric sequence

Solution:

Given geometric sequence is:

-0.6, 3 , -15, 75

We have to frame the recursive formula

Find the common ratio

$r = \frac{3}{-0.6} = -5\\\\r = \frac{-15}{3} = -5\\\\r = \frac{75}{-15} = -5$

Thus common ratio is -5

The nth term of geometric sequence is given as:

$a_n = a \times r^{n-1}$

Where,

n is the nth term

a is the first term of sequence

r is common ratio

From sequence,

a = -0.6

r = -5

Therefore,

$a_n = -0.6 \times (-5)^{n - 1}$

Where, n = 1 , 2 , 3 , 4 , .....

Thus the recursive formula is found