Question

plz solve the question

Answer 1

2). formula is n/2(2a+(n-1)d)
where a=2,d=2,n=123
3). formula is n/2(2a+(n-1)d)
where a=1,d=2,n=350/2=175
4)
let first term be a
& common difference is d
then
a+(19-1)d=52
or a+18d=52..................(1)
again
a+(38-1)d=128
or a+37d=128............(2)
(2)-(1)
37d-18d=128-52
or 19d=76
or d=4
putting the value of d in (1)
a+72=52
or a=-20
then
sum of first 56th term is
=56/2(2*(-20)+(56-1)*4)
=28(-40+220)
=28*180=5040........(ans)

generalized formula
a= first term
d= common difference ,which mean difference between every consecutive term
n=position of last term in series
sum of nth term is
=n/2(2a+(n-1)d)

formula to determine nth term is
=a+(n-1)d