If (36, p, frac{9}{4}, q) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.
-
A.
(frac{9}{16}) -
B.
(frac{81}{16}) -
C.
(9) -
D.
(9frac{9}{16})
Correct Answer: Option D
Explanation
(T_{n} = ar^{n-1}) (for an exponential sequence)
(T_{1} = 36 = a)
(T_{2} = ar = 36r = p)
(T_{3} = ar^{2} = 36r^{2} = frac{9}{4})
(T_{4} = ar^{3} = 36r^{3} = q)
(36r^{2} = frac{9}{4} implies r^{2} = frac{frac{9}{4}}{36} = frac{1}{16})
(r = sqrt{frac{1}{16}} = frac{1}{4})
( p = 36 times frac{1}{4} = 9 ; q = frac{9}{4} times frac{1}{4} = frac{9}{16})
(p + q = 9 + frac{9}{16} = 9frac{9}{16})