If 100 times the 100 text th term of an A.P. with non-zero common difference equals the 50 times its 50 text th term, then the 150 text th term of this A.P. is

Question

If 100 times the 100 text th term of an A.P. with non-zero common difference equals the 50 times its 50 text th term, then the 150 text th term of this A.P. is (A) 150 (B) zero (C) - 150 (D) 150 times its 50 text th term

Tardigrade Admin · Accepted Answer

Given 100(a+99 d)=50(a+49 d) ⇒ a+149 d=0 and T150=a+149 d =0 (Using (1))

Q. If 100 times the $10 0^{th}$ term of an A.P. with non-zero common difference equals the 50 times its $5 0^{th}$ term, then the $15 0^{th}$ term of this A.P. is

150

zero

- 150

150 times its $5 0^{th}$ term

Given $100 (a + 99 d) = 50 (a + 49 d) \Rightarrow a + 149 d = 0$
and $T_{150} = a + 149 d = 0$ (Using (1))

Q. If 100 times the 100th 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

150

zero

- 150

150 times its 50th term

Given 100(a+99d)=50(a+49d)⇒a+149d=0 and T150​=a+149d=0 (Using (1))

Q. If 100 times the $10 0^{th}$ term of an A.P. with non-zero common difference equals the 50 times its $5 0^{th}$ term, then the $15 0^{th}$ term of this A.P. is

150 times its $5 0^{th}$ term

Given $100 (a + 99 d) = 50 (a + 49 d) \Rightarrow a + 149 d = 0$
and $T_{150} = a + 149 d = 0$ (Using (1))