Question 1

What is an arithmetic sequence?

Accepted Answer

An arithmetic sequence adds a constant called the common difference d to each term. The nth term is a_n = a_1 + (n-1)d and the sum of the first n terms is S_n = n/2 * (2a_1 + (n-1)d).

Question 2

What is a geometric sequence?

Accepted Answer

A geometric sequence multiplies each term by a constant ratio r. The nth term is a_n = a_1 * r^(n-1). If r is not 1, the sum of the first n terms is S_n = a_1 * (1 - r^n) / (1 - r).

Question 3

What is the difference between a sequence and a series?

Accepted Answer

A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence. This calculator computes both the individual terms (the sequence) and the running total (the series sum).

Question 4

Can this calculator handle geometric sequences with r between -1 and 1?

Accepted Answer

Yes. It handles any common ratio including fractions, decimals and negative values. For an infinite geometric series with |r| less than 1 it will also show the closed-form limit S = a_1 / (1 - r).