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

Answer:

Recursive formula for the geometric sequence is, $a_n =-4\cdot a_{n-1} \cdot$

Step-by-step 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,

$\frac{a_2}{a_1} = \frac{8}{-2} = -4$

$\frac{a_3}{a_2} = \frac{-32}{8} = -4$ ..

Then, the recursive formula for the geometric sequence is,

$a_n = a_{n-1} \cdot (-4)$

or

$a_n =-4\cdot a_{n-1} \cdot$