The formula to find a certain number in an arithmetic sequence is an=a1+d (n-1) an=a1+d (n-1).

Solve for n

The formula of arithmetic sequence is

an = a₁ + d (n - 1)

Then we need to find the formula to determine n. I reverse the equation so the 'n' will be on the left side.

a₁ + d (n - 1) = an

Then I move all the terms on the left one by one to the right side except n

a₁ + d (n - 1) = an

d (n - 1) = an - a₁

n - 1 = (an - a₁) / d

n = 1 + (an - a₁) / d

This is the formula to solve n

n = 1 + (an - a₁) / d