Sequences Series – nth term

Find the 50th term of the following series:
1 + 3 + 7 + 13 + 21 + …………

Answer: 2451

t2 – t1= 2 (2*1)

t3 – t2= 4 (2*2)

t4 – t3  = 6 (2*3)

………………………..

…………………………

………………………..

t50 – t49= 98 (2*49)

Adding all the equations, we get

t50 – t1= 2 + 4 + 6 + ………. + 98

t50 – t1= 2450

t50 – 1 = 2450

Therefore, t50 = 2451