Given a sequence of 2,5,34,168,367,445. Determine whether is a GP or AP sequence. Give proof for your reasoning.
Given a sequence of 2,5,34,168,367,445. Determine whether is a GP or AP sequence. Give proof for your reasoning.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.6: Arithmetic Sequences As Linear Functions
Problem 1BGP
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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:
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.
For other two terms the common difference will be:
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.
Next for other terms,
As both the values of common ratio are unequal. Therefore, the given sequence is not a GP.
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