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Chapter 7: Q. 90 (page 593)

Prove that the ratio of successive terms of a nonzero geometric sequence is constant

Short Answer

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Proved

Step by step solution

Step 1. Given

Consider the geometric sequence $\{a_{k}\} = \{c r^{k}\}$

Step 2. Proof

The general term of the sequence is $\{a_{k}\} = \{c r^{k}\}$ is $a_{k} = c r^{k}$ .

The ratio of two successive terms is $\{a_{k}\} = \{c r^{k}\}$ is:

$\frac{a_{k + 1}}{a_{k}} = \frac{c r^{k + 1}}{c r^{k}} = r^{k + 1 - k} = r Thus the ratio \frac{a_{k + 1}}{a_{k}} is constant .$

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Prove that the ratio of successive terms of a nonzero geometric sequence is constant

Short Answer

Step by step solution

Step 1. Given

Step 2. Proof

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