TS ICET 2016 Question Paper with Solutions for online practice

Question : 122 of 200

Marks: +1, -0

The third and the fifth terms of a geometric progression are respectively the second and the eighth terms of an arithmetic progression whose first term and the common difference are both equal to 16. The first term of the geometric progression is

Validate

Solution:

Given : For A.P., a = d = 16.

∴a^2=a+d=32

a_8=a+7d=128

For G.P., let tn be the nth term and r the common ratio.

t_3=a_2=32

and

t_5=a_8=128

⇒t_1r^2=32

-------(i)
and,

t_1r^4=128

-----(ii)
Dividing (ii) by (i) we get

r^2=4⇒r=2

∴t_1=8

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