The sum of the first ten terms of an AP is 155 & the sum of first two terms of a GP is 9. The first term of the AP is equal to the common ratio of the GP & the first term of the GP is equal to the common difference of the AP. Find the two progressions.
Text Solution
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(3 + 6 + 12 +......) ; (2/3 + 25/3 + 625/6 +......) G.P.
(2 + 5 + 8 + .....) ; 
A.P.
Sol. Let first term of AP = a and common difference = d
∴ 
[2a + 9d] = 155 ⇒ .2a + 9d = 31
GP first term = a ′ and common ratio = r
a ′ + a ′ r = 9 ⇒ a ′ (1 + r) = 9
given a = r and a ′ = d ⇒ 2r + 9a ′ = 31
⇒ 2r + 9 . 
= 31 ⇒ 2r 2 – 29 r + 50 = 0 ⇒ r = 2, 25/2.
(i) if r = 2, So a = 2 ⇒ a ′ = 3 = d
(ii) if r = 
⇒ a = 
⇒ a ′ = 
= 
= d
So the series 3, 6, 12......... second 
, 
, 
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