Sequences & Series Formulas

Sn = a1([1-rⁿ]/[1-r])

formula for the summation of a geometric series: sum = first term([1-ratio^quantity of terms]/[1-ratio])

Sn = (n/2)(a1+an)

formula for the summation of an arithmetic series: sum = (quantity of values/2)(first term + last term)

an = a∨n-1 * r

recursive formula for a geometric sequence: nth term = previous term * common ratio

an = a∨n-1 + d

recursive formula for an arithmetic sequence: nth term = previous term + common difference

an = (a1)rⁿ⁻¹

formula for a geometric sequence: output for nth term = (first term)(common ratio)^number you're plugging in - 1

an = a1 + d(n-1)

formula for an arithmetic sequence: output for nth term = first term + (common difference)(position -1)