Question

In: Advanced Math

For the following exercises, write a recursive formula for each geometric sequence. an = {0.61, 1.83, 5.49, 16.47, ...}

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

an = {0.61, 1.83, 5.49, 16.47, ...}

Solutions

Expert Solution

Consider the following geometric sequence:

{0.61, 1.83, 5.49, 16.47,…| ...... (1)

 

The first term of above sequence is a1 = 0.61.

 

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

r = a2 ÷ a1

   = 1.83 + 0.61

   = 3

 

The recursive formula for a geometric sequence,

an = ran-1, for n ≥ 2

 

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

an = 3an-1, for n ≥ 2

 

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

a1 = 0.61

an = 3an-1, for n ≥ 2.

Junaid answered 1 year ago
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