Need help converting iterative pattern into formula

Question

var = 8

itr 1:
var == 8 (8 * 1)

itr 2:
var == 24 (8 * 3)

itr 3:
var == 48 (8 * 6)

itr 4:
var == 80 (8 * 10)

itr 5:
var == 120 (8 * 15)

Pattern: (var * (last multiplier + current iteration))

Basically I want to get the result of formula(itr) without having to iterate up to itr.

Answer 1

Use triangular numbers.

Answer 2

Multiply 8 by the sum of 1 to the current iteration:

>>> def itr(n): return 8 * sum(xrange(n+1))
...
>>> itr(1)
8
>>> itr(2)
24
>>> itr(3)
48
>>> itr(4)
80
>>> itr(5)
120

Answer 3

The value of var in the nth iteration is 8 times the sum of 1..n. The sum of 1..n is given by the formula (n)(n+1)/2; for example, the sum from 1..6 is 6*7/2 = 21.

Thus, var == 4(i)(i+1) on the ith iteration.