Question

Find no. Of terms in the sequence 1,3,6,10,15,21.........,5050

Answer 1

let y = 1+3+6+10+15+21+.........5050

y = 1+3+6 +10 +15+........T(n-1) + T(n)
now by substract both eqn
0 = 1+2+3+4+5+6+.....up to(n-1)term - T(n)
T(n) = n(n-1)/2
5050 = n(n-1)/2
10100 = n(n-1)
by heat & trial method we find
10100 = 101(101-1)
thus number of term (n)=101