Question

Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

Answer 1

Given that First term of the AP is 5.

(i)

Let the first four terms of the AP be a, a + d, a + 2d, a + 3d.

⇒ 5, 5 + d, 5 + 2d, 5 + 3d

⇒ 20 + 6d.

(ii)

Let the last four terms of the AP be a + 4d, a + 5d, a + 6d, a + 7d.

⇒ 5 + 4d, 5 + 5d, 5 + 6d, 5 + 7d.

⇒ 20 + 22d.

Now,

Given that Sum of its four terms is half the sum of the next four terms.

⇒ 20 + 6d = (1/2)(20 + 22d)

⇒ 2(20 + 6d) = 20 + 22d

⇒ 40 + 12d = 20 + 22d

⇒ 20 = 22d - 12d

⇒ 20 = 10d

⇒ d = 2.

Therefore, the common difference is 2.

Hope this helps!

Answer 2

Answer: I’ve attached a picture hope it helps :))