# In a G.P., the Ratio Between the Sum of First Three Terms and that of the First Six Terms is 125 : 152. Find Its Common Ratio. - Mathematics

Sum

In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152. Find its common ratio.

#### Solution

Let a be the first term and r be the common ratio of given G.P.
Now, sum of first three terms = S3 = (a(r^3-1))/(r-1)

Now, sum of first six terms = S6 = (a(r^6-1))/(r-1)

It is given that

((a(r^3-1))/(r-1))/((a(r^6-1))/(r-1))=125/152

=> (r^3-1)/(r^6-1)=125/152

=>(r^3-1)/((r^3)^2-(1)^2)=125/152

=> (r^3-1)/((r^3-1)(r^3+1))=125/152

=>1/(r^3+1)=125/152

=>r^3+1=152/125

=>r^3=152/125-1=(152-125)/125=27/125

=>r=3/5

Hence, the common ratio is 3/5.

Concept: Geometric Progression - Finding Sum of Their First ‘N’ Terms
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (D) | Q 9 | Page 161