Joker and jaggu.... The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.....Please don't answer
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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.
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