Question

the sum of the first 7 terms is 10 and that next 7 terms is 17.which is the first term, what is the common difference

Answer 1

write first 7 terms:-
(a-d)+(a+d)+(a+2d)+(a+3d)+(a+4d)+(a+5d)+(a+6d)=10
and solve this:-
7a+20d=10 -----------------------(1)

now the next 7 terms,
(a+7d)+(a+8d+(a+9d)+(a+10d)+(a+11d)+(a+12d)+(a+13d)=17
on solving, ,,
7a+70d=17------------------------(2)

Solve the Eqn. (1) and (2) you get the values of a and d.
on finding the first term put values of a and d in (a-d) or (a+d)