Q21 of 176 Page 8

The 4th term of an A.P. is zero. Prove that its 25th term is triple its 11th term.

Given: a₄ = 0

To Prove: a₂₅ = 3 × a₁₁

Now, a₄ = 0

⇒ a + 3d = 0

⇒ a = –3d

We know that,

a_n = a + (n – 1)d

a₁₁ = –3d + (11 – 1)d [from (i)]

a₁₁ = –3d + 10d

a₁₁ = 7d …(ii)

Now,

a₂₅ = a + (25 – 1)d

a₂₅ = –3d + 24d [from(i)]

a₂₅ = 21d

a₂₅ = 3 × 7d

a₂₅ = 3 × a₁₁ [from(ii)]

Hence Proved

Which term of the A.P. 3, 15, 27, 39, ... will be 132 more than its 54th term?

Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?

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

If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.