If 100 times the 100^th term of an AP with non zero common difference equals the 50 times its 50^th term, then the 150^th term of this AP is

–150

150

times its 50th term

0

Answer

The 150 th term of this AP
Let a be the first term and d be the common difference of the given AP, then
T₁₀₀ = a+ (100-1)d = a + 99d
T₅₀ = a +(50-1)d = a +49 d
T₁₅₀ = a + (150-1) d = a +149 d
Now, according to the question,
100 x T₁₀₀ = 50 x T₅₀
⇒ 100 (a +99d) = 50(a +49d)
2(a +99d) = (a+ 49d)
2a +198 d =a +49d
a +149d = 0