Question

The sum of third and seventh terms of an AP is 6 and their product is 8. Find

the sum of first sixteen terms of the AP.​

Answer 1

Answer:

Given:

a3+a7=6......(i)

a3×a7=8.....(ii)

Let,

a=First Term

d=Common Difference

Now,

a3=a+(3-1)d

a7=a+(7-1)d

$a_{n } = a + (n - 1)d$

Now,

From (i),

a+2d+a+6d=6

=>a+4d=3.......(3)

Again:

(a+2d)(a+6d)=8

a²+8ad+12d²=8

(3-4d)²+8(3-4d)d+12d²=8

9+16d²-24d+24d-32d²+12d²=8

4d²=1

=>d=1/2

SO,

a=1

Now,

$s_{16} =$

16/2(2×1+(16-1)1/2)

=8(30+15)/2

=180 Ans

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