Question

In an AP the sum of third and seventh term is 6 and their product is 8 find the first term and common difference of the AP

Answer 1

Let a and d be the first term and common difference of A.P.

nth term of A.P., an = a + (n – 1) d

∴ a3 = a + (3 – 1) d = a + 2d

a7 = a + (7 – 1) d = a + 6d

Given, a3 + a7 = 6

∴ (a + 2d) + (a + 6d) = 6

⇒ 2a + 8d = 6

⇒ a + 4d = 3 ...(1)

Given, a3 × a7 = 8

∴ (a + 2d) + (a + 6d) = 8

⇒ (3 – 4d + 2d) (3 – 4d + 6d) = 8 [ Using (1) ]

⇒ (3 – 2d) (3 + 2d) = 8

⇒ 9 – 4d2 = 8

⇒ 4d2 = 1

a = 3 – 4d = 3 – 2 = 1

When a = 1 and

Thus, the sum of first 16 terms of the A.P. is 76 or 20.

I hope it will help you