Question

Enter a recursive rule for the geometric sequence. 4,−16,64,−256,... a1= ; an=

Answer 1

A geometric function can be represented explicitly or recursively.

The recursive rule is: $\mathbf{a_n = -4a_{n-1} }$

The sequence is given as:

$\mathbf{4, -16, 64, -256.....}$

The terms are represented as:

$\mathbf{a_1 = 4}$

$\mathbf{a_2 = -16}$

$\mathbf{a_3 = 64}$

$\mathbf{a_4 = -256}$

Rewrite as:

$\mathbf{a_1 = 4}$

$\mathbf{a_2 = 4 \times -4}$

$\mathbf{a_3 = -16 \times -4}$

$\mathbf{a_4 = 64 \times -4}$

Substitute $\mathbf{a_3 = 64}$ in $\mathbf{a_4 = 64 \times -4}$

$\mathbf{a_4 = a_3 \times -4}$

Express 3 as 4 - 1

$\mathbf{a_4 = a_{4-1} \times -4}$

Substitute n for 4

$\mathbf{a_n = a_{n-1} \times -4}$

Evaluate the product

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

Hence, the recursive rule is: $\mathbf{a_n = -4a_{n-1} }$

Read more about geometric functions at:

brainly.com/question/222209