Question

sum of the 3rd and 7th terms of an AP is 6 and prdect is 8 find the sum of first 22 terms of the AP​

Answer 1

76 is your answer

Step-by-step explanation:

The 3rd term of an AP is a+2d and the 7th term is a+6d. So we have

the sum of 3rd term and 7th term = a+2d+a+6d = 6, or

2a+8d = 6, or

a + 4d = 3 …(1)

Their product is (a+2d)*(a+6d) = 8 …(2)

From (1), a = 3–4d. Put that in (2) to get

(a+2d)*(a+6d) = 8, or

(3–4d+2d)*(3–4d+6d) = 8, or

(3–2d)*(3+2d) = 8, or

9–4d^2 = 8, or

4d^2 = 1, or

d^2 = 1/4, or

d = 1/2.

From (1), a = 3–4d = 3–2 = 1.

The sum of the first 16 terms

S16 = (n/2)[2a+(n-1)d]

= (16/2)[2*1 + (16–1)*1/2]

= 8[2+15/2]

= 8 *19/2

= 76

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Answer 2

Hope my answers helps you.