the sum of 3 terms of gp is 7 and that of 6 terms is 63. find gp
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nth term of the G.P. is given to be 2^n. Setting n=1,2,3,…. we find that
First term of the G.P. is 2^1 = 2;
Second term of the G.P. is 2^2 = 4;
Third term of the G.P. is 2^3 = 8.
G.P. is, therefore 2,4,8,16,32,64,…..
For this G.P., first term a = 2, and common ratio r = 2.
Sum of the first n terms of a G.P. with first term “a” and common ratio “r” is given by
S = a(r^n - 1)/(r - 1).
To find the sum of first 6 terms of the G.P. with first term “2” and common ratio “2” , we set a = 2, r = 2, n = 6.
S = 2(2^6 - 1)/(2 - 1) = 2(64 - 1)/(1) = 2(63) = 126.
Sum of the first 6 terms of this G.P. is, therefore, 126.
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