HOTS : PROGRESSION & SERIES

Prob 1.  Find the numbers a, b, c between 2 and 18 such that (i) their sum is 25 ,

(ii) the numbers 2, a, b are consecutive terms of an A.P. and

 (iii) the numbers b,c,18 are consecutive terms of a G.P.

 

Sol.   

We have a + b + c = 25          . . . (1)

2 , a , b are in A.P.

⇒  2a = 2 + b                . . . (2)

Also b, c, 18 are in G.P

⇒    18b = c2            . . . (3)

Substituting for a and b in (1),  (using relations (2)  and (3)),  we get

c2 + 12c – 288 = 0

⇒ (c – 12) (c + 24) = 0

⇒ c = 12, or – 24

Since the numbers lie between 2 and 18,

we take c = 12 ,

⇒ b = 8, a = 5.

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