Question

If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.

Options

• 5

• 0

• 4

• 2

Answer 1

If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is 0.

Explanation:

Given, in AP

9 times nineth term is equal to 13 times thirteenth term

∴ 9a₉ = 13a₁₃

9(a + 8d) = 13(a + 12d)

9a + 72d = 13a + 156d

13a − 9a = − 156d + 72d

4a = − 84d

a = − 21d

a + 21d = 0

a₂₂ = 0

∴ Twenty second term = 0