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.
8/5
8/3
72/25
56/9
Correct answer is C
Let the common ratio be r so that the first term is 2r.
Sum, s = a1−r
ie. 8 = 2r1−r
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
= 85 + 3225
= 40+3225
= 7225
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