Math, asked by rvedhapriya7252, 1 year ago

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 ?

Answers

Answered by amikkr
16

The common ratio is 1/3.

  • Let the given geometric series be a,ar,ar²,ar³,...,ar^n.

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 (\frac{r}{1-r})                   (Sum of n terms of GP is \frac{first \ term}{1 - common \ ratio})

1 - r = 2r

1 = 3r

r = 1/3

  • The common ratio is 1/3.
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