Geometric Sequence

It is not “necessary” to remember the formula, but you can easily derive it if a question requires its knowledge.

Let the geometric sequence be a, ar, ar^2, ar^3….
So the nth term is ar^(n-1).
Or the sum to n terms given by S = a + ar + ar^2 + ar^3 +…+ar^(n-2) + ar^(n-1).---------(1)
Now, multiply both sides of the equation by r and we get
Sr = ar + ar^2 + ar^3+…+ar^(n-1) + ar^n.-------------(2).
Subtracting (2) from (1), we get that S – Sr = a – ar^n (all other terms will cancel out).
Or S(1-r) = a(1 – r^n).
Or S = a(1 – r^n)/(1-r).