If 100 times the 100th term of an A.P.

Question

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

Accepted Answer

$$100a_{100}=50a_{50} \Rightarrow 100(a+99d)=50(a+49d) \Rightarrow 2a+198d=a+49d \Rightarrow a+149d=0.$$

$T_{150}=a+149d=0.$

Solutions · 1