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The first term of a geometric progression is twice its co...

The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the G.P if its sum to infinity is 8.

A.

8/5

B.

8/3

C.

72/25

D.

56/9

Correct answer is C

Let the common ratio be r so that the first term is 2r.

Sum, s = a1r

ie. 8 = 2r1r

8(1-r) = 2r,

8 - 8r = 2r

8 = 2r + 8r

8 = 10r

r = 45.

where common ratio (r) = secondterm(n2)firstterm(a),

r = n22r

r = 45 and a = 2r or 85

45 * 85 = n2

3225 = n2

The sum of the first two terms = a + n2

= 853225

40+3225

7225