If the first term of an infinite gp is 1 and each term is twice the sum of the succeeding terms then the common ratio is ?
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The common ratio is 1/3.
- Let the given geometric series be a,ar,ar²,ar³,...,.
First term is a and common ratio is r.
But the first term is 1.
- Therefore, the series becomes 1,r,r²,r³,....
- The first term is equal to twice the sum of the succeeding terms
1 = 2(r+r²+r³+....)
1 = 2 () (Sum of n terms of GP is )
1 - r = 2r
1 = 3r
r = 1/3
- The common ratio is 1/3.
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