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

The rule of the geometric sequence is $a* r^{n-1}$
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio

Given: the fourth term (a4) = 121.5   and the common ratio = 3  and   n = 4

∴ $121.5 = a* 3^{4-1}$
∴ a = 121.5/3³ = 121.5/27 = 4.5

So, The formula for this sequence will be    $4.5 * 3^{n-1}$

Answer 2

Answer:

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.