Question

20) Write the explicit formula for the geometric sequence defined as an

Answer 1

a1=1/8 • 2(n-1)

Step-by-step explanation:

So the formula for the explicit is
An=a1 • r (n-1) where a1 is the first term which is 1/8 and multiplied by r which is the term, it is going by 2 which is the term its multiplied by and then (n-1)
An= a1 • r (n-1)

A1= 1/8 • 2(n-1)

Answer 2

• aₙ = 2ⁿ⁻⁴

Step-by-step explanation:

According to the recursive formula we have a GP with:

• The first term a₁ = 1/8
• The common ratio r = 2

The explicit formula is:

• aₙ = a₁*rⁿ⁻¹

Substitute the value to get:

• aₙ = 1/8*2ⁿ⁻¹ = 2⁻³*2ⁿ⁻¹ = 2ⁿ⁻⁴