Question

. The three consecutive terms of an
exponential sequence (G.P) are the
second, third and sixth terms of a linear
sequence (A.P). Find the common ratio
of the exponential sequence.

Answer 1

The terms of the geometric series may be: a , ab , ab^2 .
The 2. , 3. , 6. term of the arithmetic series may be: c , c+d , c+4d
i.e. a = c , ab = c+d , ab^2 = c+4d
==> ab = a+d ==> d = ab-a
==> ab^2 = a+4(ab-a) = 4ab-3a
==> b^2 = 4b-3
==> b^2-4b+3 = 0
==> (b-3)(b-1) = 0
==> b = 3 or b = 1