Question

14. In an A.P consisting of 27 terms, the sum of the first three terms is 21 and that of the three middle terms is 93. Find the first term and the common
difference.​

Answer 1

Answer:

Let the three terms of A.P are a,a+d,a+2d.

Now,As per the question ,

a+a+d+a+2d=3a+3d=21

i.e. a+d=7 or, 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−a

2

=13

a

2

−14a+13=0

By factorising,we get

a=13,1

d=7−a

For a=13,1d=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