Math

Sequence Calculator

Find the nth term and partial sum of an arithmetic or geometric sequence.

First term

Common difference / ratio

Term number n

Type

Calculated Output

nth term 17

Sum of first n terms 57

Formula: Arithmetic: a+(n−1)d · Geometric: a·rⁿ⁻¹

Step-by-Step Breakdown

1. Values used:

2. First term = 2

3. Common difference / ratio = 3

4. Term number n = 6

6. nth term = 17

7. Sum of first n terms = 57

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The math behind it

Arithmetic: nth term a + (n−1)d, sum n/2·(first + last). Geometric: nth term a·rⁿ⁻¹, sum a(rⁿ − 1)/(r − 1).

Arithmetic 2, d = 3, n = 6 → term 17, sum 57.

When does a geometric sum converge?

An infinite geometric series converges only when |r| < 1.