Chapter 12: Q 23. (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
$a_{1} = \sqrt{2}, r = \sqrt{2}$

Short Answer

Expert verified

The $n t h$ term is $a_{n} = {\sqrt{2}}^{n}$ and the fifth term is $a_{5} = 4 \sqrt{2}$ .

Step by step solution

Step 1. Given information.

We have,

$a_{1} = \sqrt{2}, r = \sqrt{2}$

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

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

Substitute $a_{1} = \sqrt{2}, r = \sqrt{2}$ and $n = 5$

$a_{n} = \sqrt{2} {(\sqrt{2})}^{n - 1} a_{n} = {\sqrt{2}}^{n}$

and

role="math" localid="1647002123469" $a_{5} = \sqrt{2} {(\sqrt{2})}^{5 - 1} a_{5} = \sqrt{2} {(\sqrt{2})}^{4} a_{5} = 4 \sqrt{2}$

a_{1} = \sqrt{2}, r = \sqrt{2}

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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
$a_{1} = \sqrt{2}, r = \sqrt{2}$

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=2

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

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Mechanics Maths

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Theoretical and Mathematical Physics

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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
$a_{1} = \sqrt{2}, r = \sqrt{2}$