Question

If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

10 × a₁₀ = 15 × a₁₅   ...(Given)

⇒ 10(a + 9d) = 15(a + 14d)   ...[a_n = a + (n – 1)d]

⇒ 2(a + 9d) = 3(a + 14d)

⇒ 2a + 18d = 3a + 42d

⇒ a = –24d

⇒ a + 24d = 0

⇒ a + (25 – 1)d = 0

⇒ a₂₅ = 0 

Hence, the 25^th term of the AP is 0.