Question

Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your answer.

Answer 1

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Explanation:

sample answer on edge ;)

Answer 2

`a_n = 4.5 * 3^(n-1)`

Explanation:

Given

`a_4 = 121.5`

`r = 3`

Required

`a_n = a_1 * r^(n -1)`

Substitute 4 for n in
`a_n = a_1 * r^(n -1)`

`a_4 = a_1 * r^(4 -1)`

`a_4 = a_1 * r^3`

Substitute 121.5 for
`a_4`

`121.5 = a_1 * 3^3`

`121.5 = a_1 * 27`

Solve for a1

`a_1 = (121.5)/(27)`

`a_1 = 4.5`

So, we have:

`a_n = a_1 * r^(n -1)`

`a_n = 4.5 * 3^(n-1)`