Understanding and Using the Explicit Formula for Arithmetic Sequences: An In-depth Guide

Explicit Formula for Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The explicit formula for an arithmetic sequence is used to find any term in the sequence without having to list all the preceding terms.

The explicit formula for an arithmetic sequence is given by:

An = A1 + (n – 1) * d

where:
– An represents the nth term in the sequence
– A1 is the first term in the sequence
– n is the position of the term in the sequence
– d is the common difference between consecutive terms

To use the explicit formula, you need to know the first term (A1), the position of the term you want to find (n), and the common difference (d).

Let’s consider an example:

Find the 7th term of an arithmetic sequence with a first term of 3 and a common difference of 5.

Using the explicit formula, we have:

A7 = A1 + (7 – 1) * d

Substituting the given values into the formula, we get:

A7 = 3 + (7 – 1) * 5

Simplifying further:

A7 = 3 + 6 * 5

A7 = 3 + 30

A7 = 33

Therefore, the 7th term of the arithmetic sequence is 33.

It is important to note that the explicit formula only works for arithmetic sequences, where the difference between consecutive terms is constant.

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