The number of terms common between the series 1+ 2 + 4 + 8..... to 100 terms and 1 + 4 + 7 + 10 +... to 100 terms is

Options

A. 6
B. 4
C. 5
D. none of these

Answer

C

Explanation

For G.P., `t_(n)=2^(2n-1),` for A.P., `T_(m)=1+(m-1)3=3m-2`.
They are common if `2^(n-1)=3m-2`. For G.P. `100^(th)` term is `2^(99)`. For A.P. `100^(th)` term is 1+(100-1)3=298. Now we must choose value of m such that 3m-2 is of the form `2^(n-1)`. Hemce, 3m-2=1,2,3,8,16,32,64,128,256 for which m=1,4/3,2,10/3,6,34/3,22,130/3,86. Hence, possible values of m are 1,2,6,22,86. Hence, there are five common terms.