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

Engineering

Mathematics

Arithmetic Progression and Its Properties

Question

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

zero

–150

150 times its 50^th term

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100 (a + 99d) = 50 (a + 49d)

$∴$ a + 149d = 0 .......(A)

and

T₁₅₀ = a + 149d = 0 [From (A)].

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