9303753286127016 If the sum of first 6 terms is 9 times to the sum of first 3 terms of the same G.P., then common ratio of the series will be

If the sum of first 6 terms is 9 times to the sum of first 3 terms of the same G.P., then common ratio of the series will be

 If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the sequence is called a geometric progression. (GP), whereas the constant value is called the common ratio. 

The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:

a, ar, ar2, ar3, ar4, and so on.

Sum of GP for Infinite Terms

If the number of terms in a GP is not finite, then the GP is called infinite GP. The formula to find the sum of an infinite geometric progression is

Sn = a(rn-1)/(r-1), where a is the first term and r is the common ratio.

Here,

Sn = Sum of n terms geometric progression

a = First term of G.P.

r = Common ratio of G.P.

n is number of terms

Solution

Let a be the first term and r be the common ratio of the GP.

Sum of n terms of GP, Sn = a(rn-1)/(r-1)

Given S6 = 9S3

a(r6-1)/(r-1) = 9 a(r3-1)/(r-1)

(r6-1) = 9 (r3-1)

(r3-1)(r3+1) = 9(r3-1)

(r3+1) = 9

r3 = 8

r = 2

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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