Question

If the sum of the first n terms of an ap is 4n-n^2, what is the first term? What is the sum of first two terms? What is the second term?Similarly, find the 3rd, 10th and nth terms.

Answer 1

let first term is a
& common difference be d
then sum of nth term is
= n/2*(2a+(n-1)d)..........(1)
then
n/2*(2a+(n-1)d)=4n-n²
or 2a+(n-1)d=8-2n............(2)
then putting the value of n =1 in (2)
gives 2a=8-2

or a=3............(ans)
putting the value of a & n=2
gives 2*3-d=8-4

or d=6-4=2
then putting the value of a=3,d=2&n=2 in (1)
gives 2/2(2*3+(2-1)*2)=6+2=8...........(ans)
second term =8-3=5....................(ans)
third term =3+(3-1)*2
=3+4=7...................(ans)
10 th term =3+(10-1)*2
=3+18=21...........(ans)
nth term=3+(n-1)*2
=3-2+2n=1+2n.............(ans)