If 100 times the 100th term of an AP

• Sequences Series

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

1. 0
2. 150
3. -150
4. 150 times its 50^th term

Answer

100(T₁₀₀) = 50(T₅₀)

2[a + 99d] = a + 49d

a + 149d = 0  

T₁₅₀ = 0

The correct option is A.