The 4th term of an AP is zero, Prove that its 25th term is triple its

1.	The 4th term of an AP is zero, Prove that its 25th term is triple its 11th term.
Answer» Let a be the first term and d be the common difference of an AP. a₄ = a + (n- 1)d = a + (4 – 1)d = a + 3d Since 4th term of an AP is zero. a + 3d = 0 or a = -3d ….(1) Similarly, a₂₅ = a + 24d = -3d + 24d = 21d …(2) a₁₁ = a + 10d = -3d + 10d = 7d ….(3) From (2) and (3), we have a₂₅ = 3 x a₁₁ Hence proved.

The 4th term of an AP is zero, Prove that its 25th term is triple its 11th term.

Answer»

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

a₄ = a + (n- 1)d

= a + (4 – 1)d

= a + 3d

Since 4th term of an AP is zero.

a + 3d = 0

or a = -3d ….(1)

Similarly,

a₂₅ = a + 24d = -3d + 24d = 21d …(2)

a₁₁ = a + 10d = -3d + 10d = 7d ….(3)

From (2) and (3), we have

a₂₅ = 3 x a₁₁

Hence proved.