Chapter 12: Q 17. (page 824)

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given. $a_{1} = 2, r = 3$

Short Answer

Expert verified

The $n t h$ term is $a_{n} = 2 \times 3^{n - 1}$ and the fifth term is $a_{5} = 162$ .

Step by step solution

Step 1. Given information.

We have $a_{1} = 2$ and $r = 3$

The $n t h$ term of a geometric sequence is determined by formula $a_{n} = a_{1} r^{n - 1}$ . $a_{1} = 2$

Step 2. To find the fifth term and the nth term.

Substitute $a_{1} = 2, r = 3$ and $n = 5$ .

$a_{n} = 2 \times 3^{n - 1}$

and

$a_{5} = 2 \times 3^{5 - 1} a_{5} = 2 \times 3^{4} a_{5} = 162$

The $n t h$ term is $a_{n} = 2 \times 3^{n - 1}$ and the fifth term is $a_{5} = 162$ .

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Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given. $a_{1} = 2, r = 3$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the fifth term and the nth term.

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Find the fifth term and the nth term of the geometric sequence whose initial term a1and common ratio rare given. a1=2,r=3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. To find the fifth term and the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Geometry

Theoretical and Mathematical Physics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the fifth term and the nth term of the geometric sequence whose initial term $a_{1}$ and common ratio $r$ are given. $a_{1} = 2, r = 3$