Let-a-b-and-c-form-a-GP-of-common-ratio-r-with-0-lt-r-lt-1-If-a-2b-and-3c-form-an-AP-then-r-equals-

Question Number 56420 by gunawan last updated on 16/Mar/19

Let a, b and c form a GP of common ratio r,

with 0 < r < 1 . If a, 2 b and 3 c form an AP,

then r equals

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19

a = a

b = a r

c = {a r}^{2}

2 (2 b) = a + 3 c

2 (2 a r) = a + 3 ({a r}^{2})

4 r = 1 + 3 r^{2}

3 r^{2} - 3 r - r + 1 = 0

3 r (r - 1) - 1 (r - 1) = 0

(r - 1) (3 r - 1) = 0

r \neq 1 [g i v e n i n q u e s t i o n]

r = \frac{1}{3}