Question

the sum og first term of an ap is 10 that of next 7terms is 17. find AP

Answer 1

Hey mate..
==========
We know,

The formula to finding the sum of an AP

= n/2 { 2a + (n-1) × d }

A/Q,

S(7) = 10= 7 (2a+6 d ) / 2

=>10=7(a+3d)

=>10/7 -3d = a.....(1)

And, the next 7 terms of an AP.

S(27) = 17+10 = 14 (2a+13 d ) / 2

27 = 7 (2a+13 d ) .....(2)

By putting the value of a in Eq.(2) we will get,

27 = 7 (2(10/7 - 3d)+13 d )

=>27/7 = 2(10/7 - 3d)+13 d

=>27/7=20/7 -6d +13d = 20/7+ 7d

=>27/7 - 20/7 = 7d

=> 1/7 = d

Putting this value in eq.(1),

=> 10/7 -3d = a

=> a=10/7 -3/7 = 1

so, a=1 and d=1/7

Hence , The AP is 1 , 1 + 1/7 = 8/7 , 9/7 , 10/7.....

Hope it helps !!