Find the nth term of 2, 8, 18, 32, 50

From the series,  2, 8, 18, 32, 50,...

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third, n =3,                = 2*3*3 = 18

Third term, n = 4,       = 2*4*4 = 32

Fourth term, n =5,     2 * 5* 5 = 50

For nth term,        2 *n *n = 2n²

Therefore nth term =  2n²

I hope this helps.