find a quadratic model and term number the last given for 10,12,16,22,30,40,....516
The terms are
2*(5+0)
2*(5+1)
2*(5+3)
2*(5+6)
2*(5+10)
Look familiar?
0,1,3,6,10,... = 0+1+2+3+4+... = n(n-1)/2
Tn = 2(5 + n(n-1)/2)
2(5 + n(n-1)/2) = 516
5+n(n-1)/2 = 258
n(n-1)/2 = 253
n(n-1) = 506 = 23*22
So, T23 = 516