Answered: Given a sequence of 2,5,34,168,367,445.…

Name: Given a sequence of 2,5,34,168,367,445. Determine whether is a GP or A
Uploaded: 2024-03-20T06:38:58.000Z
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Description: Given a sequence of 2,5,34,168,367,445. Determine whether is a GP or AP sequence. Give proof for your reasoning.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Given a sequence of 2,5,34,168,367,445. Determine whether is a GP or AP sequence. Give proof for your reasoning.

Expert Solution

Step 1

The sequence is given as:

$2, 5, 34, 168, 367, 445$

PART A

To check that whether the given sequence is AP or not.

For a sequence to be a AP the common difference between the terms of the sequence should be same.

$\begin{array}{rcl} d & = & a_{2} - a_{1} \\ = & 5 - 2 \\ = & 3 \end{array}$

For other two terms the common difference will be:

$\begin{array}{rcl} d & = & a_{3} - a_{2} \\ = & 34 - 5 \\ = & 29 \end{array}$

As both the values of d are not equal therefore the common difference is not same. Therefore the given sequence is not an AP.

Step 2

PART B

To check that the given sequence is GP or not.

To be a GP a sequence has same common ratio.

$\begin{array}{rcl} r & = & \frac{a_{2}}{a_{1}} \\ = & \frac{5}{2} \end{array}$

Next for other terms,

$\begin{array}{rcl} r & = & \frac{a_{3}}{a_{2}} \\ = & \frac{34}{5} \end{array}$

As both the values of common ratio are unequal. Therefore, the given sequence is not a GP.

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