Question

if 9times the 9th term in an a.p.is equal to 15times the 15 term in the a.p what is the 24 th term

Answer 1

We have,
9a₉ = 15a₁₅
⇒9(a + 8d) = 15(a + 14d)
⇒9a + 72d = 15a + 210d
⇒15a - 9a + 210d -72d = 0
⇒6a + 138d = 0
⇒a + 23d = 0
⇒a₂₄ = 0

Thus the 24th term is 0.