Question

Write the recursive formula for the geometric sequence. a1 = -2 a2 = 8 a3 = -32

Answer 1

a1 = -2
an = (-4)•an-1

Answer 2

Recursive formula for the geometric sequence is,
`a_n =-4\cdot a_(n-1) \cdot`

Explanation:

A geometric sequence states that a sequence in which the ratio of any term to the previous term is constant.

A recursive formula states that it uses the preceding term to define the next term of the sequence.

For the geometric sequence, the recursive formula is given by;

`a_n = a_(n-1) \cdot r` where r is the common ratio.

Given the following:

`a_1 = -2`,
`a_2 = 8` and
`a_3 = -32`

The common ratio for the geometric sequence , r =-4

Since,

`(a_2)/(a_1) = (8)/(-2) = -4`

`(a_3)/(a_2) = (-32)/(8) = -4` ..

Then, the recursive formula for the geometric sequence is,

`a_n = a_(n-1) \cdot (-4)`

or

`a_n =-4\cdot a_(n-1) \cdot`