Let S(n)=n^2+3n be the sum of the first n terms of a sequen

i)Find the sum of T(1)+T(2)+...+T(10).
S(10)=10^2+3(10)=130

(ii)Find the sum of T(1)+T(2)+....+T(9).
S(9)=9^2+3(9)=108

(iii)Hence find T(10).
T(10)=S(10)-S(9)=22

b)Find T(n).
T(1)=S(1)=4
T(2)=S(2)-S(1)=10-4=6
T(3)=S(3)-S(2)=18-10=8
T(4)=S(4)-S(3)=28-18=10
T(5)=S(5)-S(4)=40-28=12
and so on
T(n)=2(n+1)
S(n)=[4+2(1+n)]n/2=(2+1+n)n=n^2-3n
c)What kind of sequence is T(1),T(2),T(3),....?
AP

a(i)T(1)+T(2)+...+T(10)
=S(10)
=10^2+3x10
=130

(ii)T(1)+T(2)+....+T(9)
=S(9)
=9^2+3x9
=108

(iii)T(10)
=S(10)-S(9)
=22

bT(n)=S(n)-S(n-1)
=n^2+3n-(n-1)^2-3(n-1)
=2n+2

c.arithmetic sequence