If 100 times the 100 th term of an A.P with non- zero common difference equals the 50 times its 50th term,then the 150th term of this A.P is
a. 150 times its 50th term
b. `150`
c. `0`
d. `-150`

Options

A. 150 times its 50th term
B. 150
C. zero
D. -150

Answer

C

Explanation

Let a be the first term and d be the common difference. Then,
`100T_(100)=50T_(50)`
`implies 100(a+99d)=50(a+49d)`
`implies 2(a+99d)=(a+49d) implies a+149d=0`
`:. T_(150)=0`.