Question

the sum of 4th and 8th term of an AP is 24. The sum of the 6th and 10th term is 32. find the 26th term.

Answer 1

I hope it will help you

Answer 2

Answer:

52

Step-by-step explanation:

Let a be the first term and d be the common difference.

(i) Sum of 4th term and 8th term is 24.

∴ a₄ + a₈

⇒ 24 = [a + (4 - 1) * d] + [a + (8 - 1) * d]

⇒ 24 = a + 3d + a + 7d

⇒ 24 = 2a + 10d

⇒ a + 5d = 12.

(ii) Sum of 6th term and 10th term is 32:

∴ a₆ + a₁₀

⇒ 32 = [a + (6 - 1) * d] + [a + (10 - 1) * d]

⇒ 32 = a + 5d + a + 9d

⇒ 32 = 2a + 14d

⇒ a + 7d = 16

On solving (i) & (ii), we get

a + 5d = 12

a + 7d = 16

----------------

      -2d = -4

          d = 2.

Substitute d = 2 in (i), we get

⇒ a + 5d = 12

⇒ a + 10 = 12

⇒ a = 2

∴ 26th term of the AP:

a₂₆ = a + (26 - 1) * d

     = 2 + (26 - 1) * 2

     = 2 + 25 * 2

     = 52.

Therefore, 26th term is 52.

Hope it helps!