# [Solved] If K+1 2k-1 3k+1 Are Three Consecutive Terms Of Geometric Progression, Find The Possible Values Of The Common Ratio

Given the three terms of the GP: �+1,2�−1,3�+1K+1,2K−1,3K+1

Step 1: Find the ratio using the first two terms: �=2�−1�+1r=K+12K−1​

Step 2: Find the ratio using the last two terms: �=3�+12�−1r=2K−13K+1​

Step 3: Equate the two expressions for �r: 2�−1�+1=3�+12�−1K+12K−1​=2K−13K+1​

Now, let’s solve for �K in this equation.

Finished working

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The simplified solutions for �K are �=0K=0 and �=8K=8.

Now, using these values for �K, let’s find the corresponding values for the common ratio �r in a simplified manner.

Step 4: Plug the values of �K into the expression for �r:

�=2�−1�+1r=K+12K−1​

Let’s calculate �r for both values of �K.

Finished working

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The simplified values for the common ratio �r based on the values of �K are:

1. �=−1r=−1 when �=0K=0
2. �=53r=35​ (or 1.67) when �=8K=8

Thus, the possible values for the common ratio are �=−1r=−1 and �=53r=35​.