Find a formula for the nth term of the geometric sequence. Then find the indicated term of the...
Question:
Find a formula for the {eq}n {/eq}th term of the geometric sequence. Then find the indicated term of the geometric sequence.
10th term: 5, 30, 180,...
Geometric Sequence:
In a geometric sequence, the quotient of any two consecutive terms is always equal to the common ratio {eq}r {/eq}. If the first term is {eq}a_1 {/eq}, then the general term of a geometric sequence is obtained using the formula:
$$a_n = a_1 r^{n-1} $$
When {eq}r {/eq} is negative, an alternating sequence is created as the terms will alternate between negative and positive.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerFirst, we'll obtain the general term using {eq}a_1 = 5 {/eq} and {eq}r= \displaystyle \frac{30}{5}=6 {/eq}, which is the ratio of the first two...
See full answer below.
Learn more about this topic:
from
Chapter 27 / Lesson 26Learn about geometric sequences. Understand what a geometric sequence is, learn how to find the common ratio of a geometric sequence, and see examples.