*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 = c^{2} . . . (3)

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

c^{2} + 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.