Math Problem Statement

The 17th term in a geometric sequence is 15. When the common ratio is 0.2, what is the 18th term?

Solution

We are given that the 17th term of a geometric sequence is 15, and the common ratio is r=0.2r = 0.2. The task is to find the 18th term.

In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. So, the relationship between consecutive terms is:

an+1=an×ra_{n+1} = a_n \times r

To find the 18th term (a18a_{18}), we use the formula:

a18=a17×ra_{18} = a_{17} \times r

Given that a17=15a_{17} = 15 and r=0.2r = 0.2:

a18=15×0.2=3a_{18} = 15 \times 0.2 = 3

Thus, the 18th term is 33, which matches the first answer option.

Let me know if you need more details or explanations!

Related Questions:

  1. What is the general formula for the nn-th term of a geometric sequence?
  2. How do you find the sum of a finite geometric series?
  3. What happens to the terms of a geometric sequence if the common ratio is negative?
  4. How does the common ratio affect the convergence of an infinite geometric sequence?
  5. Can a geometric sequence have a common ratio of 1 or 0?

Tip: In geometric sequences, if the common ratio is less than 1, the terms decrease as the sequence progresses.

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Math Problem Analysis

Mathematical Concepts

Geometric Sequence
Common Ratio

Formulas

a_{n+1} = a_n * r
a_{18} = a_{17} * r

Theorems

Geometric Sequence Term Formula

Suitable Grade Level

Grades 8-10