Question

In: Advanced Math

For the following exercises, write a recursive formula for each geometric sequence.

For the following exercises, write a recursive formula for each geometric sequence.

Solutions

Expert Solution

Consider the following geometric sequence:

{-2, 4/3, -8/9, 16/27, …} ...... (1)

 

The first term of above sequence is a1 = 2

 

Common ratio of the above sequence will be obtained by dividing its second term by the first term,

r = a2 ÷ a1

   = 4/3 ÷ (-2)

   = -2/3

 

The recursive formula for a geometric sequence is,

an = ran-1, for n ≥ 2

 

Substitute r = -2/3, the recursive formula for the nth term of the geometric sequence will be,

an = -2/3an-1, for n ≥ 2

 

Therefore, the recursive formula for the above geometric sequence is,

a1 = -2

 an = -2/3an-1, for n ≥ 2.

Junaid answered 1 year ago
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