Question

In an AP 3rd term is 7 & the 7th term is 2 more than three times the third term find the sum of first 20 terms of an AP​

Answer 1

Answer:

Step-by-step explanation:

let the first term be a

And common difference be d

3rd term =3(7th term)

And if 8th term is -12

That means a+7d=-12

So,

a+2d=3(a+6d)

a+2d=3a+18d

a-3a=18d-2d

-2a=16d

a=-8d

Putting the value of a in a+7d=-12

-8d+7d=-12

-d=-12

d=12

a=-96 (a=-8(12))

Now calculating the sum of first 30 terms of an AP

Given n=30 , a=-96 , d=12

Sn=n/2(2a+(n-1)d)

=30/2(2(-96)+(30–1)12)

=15(-192+(29)(12))

=15(-192+348)

=15(156)

=2340

So the sum of first 30 terms is 2340