Geometric Sequence Nth Term Calculator

About this calculator

Any term of a geometric sequence can be found directly, without listing every term before it, using the formula a(n) = a1 × r^(n−1), where a1 is the first term, r is the common ratio, and n is the position of the term you want. This closed-form formula is what makes geometric sequences practical to work with even when n is very large.

Students use it to jump straight to a distant term in algebra homework instead of multiplying by r repeatedly, and the same formula underlies real compounding calculations — projecting the value of an investment after n compounding periods, modeling exponential population or bacterial growth at a given time step, or computing depreciation of an asset that loses a fixed percentage of its value each year.

This calculator takes the first term, common ratio, and the term position you want and returns that term’s value.