Question

Write the recursive definition for the geometric sequence. Then write the exponential equation using regression

Answer 1

The geometric sequence 128,32,8,2 has a common ratio

The recursive definition of the geometric sequence is $a_n = 4a_{n-1}$ where a1 = 128

How to determine the recursive definition?

The geometric sequence is given as:

128,32,8,2

Start by calculating the common ratio (r)

$r = \frac{a_{n}}{a_{n-1}}$

Substitute 2 for n

$r = \frac{a_2}{a_1}$

Substitute known values

$r = \frac{128}{32}$

Evaluate the quotient

$r = 4$

Substitute 4 for r in $r = \frac{a_{n}}{a_{n-1}}$

$4 = \frac{a_{n}}{a_{n-1}}$

Cross multiply

$a_n = 4a_{n-1}$

Hence, the recursive definition of the geometric sequence is $a_n = 4a_{n-1}$ where a1 = 128

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