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

Answer:

$a_n = 4.5 * 3^{n-1}$

Step-by-step 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

$a_1 = \frac{121.5}{27}$

$a_1 = 4.5$

So, we have:

$a_n = a_1 * r^{n -1}$

$a_n = 4.5 * 3^{n-1}$