Question

the sum of three term of am AP is 21 and the product of the frist and third term exceeds the second term by 6. find the sum of 20 term of the AP
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Answer 1

Let the three terms of A.P are

a,a+d,a+2d.

Now,

a+a+d+a+2d=3a+3d=2

i.e. a+d=7

d=7−a.

Now,

a(a+2d)−(a+d)=6

a{a+2(7−a)}−7=6

a{a+14−2a}=13

a{14−a}=13

14a-a² =13

a²-14a = 13

On factorising

a² − 14a+13=0

We get

a=13,1

a=13,1d=7−a

For a=13,1

d=7−13,7−1=−6,6 respectively.

Now, there are two AP's a,a+d,a+2d for two values of a and d

13,7,1 and 1,7,13