Question

Write the mathematical expression that describes the arithmetic sequence

Answer 1

There are three types of progression: arithmetic progression, geometric progression and harmonic progression. Arithmetic progression is a sequence of numbers or variables that has a common difference. Geometric progression has a common ratio, while harmonic progression is just the reciprocal of the sequence in arithmetic progression.

Example of an arithmetic sequence is: 34, 37, 40, 43, 46. The adjacent terms have a common difference of 3. Mathematicians have already derived equations for arithmetic progression so it would be just convenient for us to predict the next numbers or missing numbers in the sequence. These equations are:

An = A1 + (n-1)d
Sn = (n/2)(A1 + An)

where
An is the nth term in the sequence
A1 is the first term in the sequence
n is the total number of terms int he sequence
d is the common difference
Sn is the sum of all the terms in the sequence

These two equations describe an arithmetic sequence.