## Arithmetic Geometric Harmonic Fibonacci Sequence: Introduction

## FAQs on Difference Between Sequence and Series

1. What is the Fibonacci sequence?

The Fibonacci sequence is a recursive sequence where each term is the sum of the two preceding terms (e.g., 1, 1, 2, 3, 5, 8, 13...).

2. Write the formula for the geometric series.

The sum of a geometric series can be computed using the formula:

Sn = [a1(rn-1)]/(r-1)

Here, Sn = The partial sum of the geometric series up to the nth term.

a1 = First term.

r = Common ratio.

3. What are some tests for determining the convergence of an infinite series?

Various tests exist to determine the convergence or divergence of an infinite series. These include the ratio test, the comparison test, the integral test, and the alternating series test, among others.

4. Define an arithmetic sequence.

In an arithmetic sequence, each term is obtained by adding a constant difference, known as the common difference, to the preceding term. For example, the sequence {2, 5, 8, 11, ...} is an arithmetic sequence with a common difference of 3.

5. Write the formula for the arithmetic series.

The sum of an arithmetic series can be calculated using the formula:

Sn = (n/2)[2a1+(n-1)d]

Here, Sn = The partial sum of the arithmetic series up to the nth term.

a1 = First term.

d = Common difference.