Question

The sum of 3rd and 7th terms of an A.P is 6 and their profuct is 8.find the sum of first 20 terms of the A.P

Answer 1

let the first term be 'a' and common difference be 'd'.
According to the question,
a+2d + a +6d =6
2a +8d =6
a+4d =3
a2 + 16d2 +8ad =9..........equation 1
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(a+2d)(a+6d)=8
a2 +8ad +12d2=8...........equation 2
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Subtracting equation 2 from 1
4d2 =1
d2=1/4
d=1/(+-2)
if d=2
a will be a=1
sum of 20 terms=400
if d=-2
a=11
sum of 20 terms = -160