How to Find the nth Term of an Arithmetic Sequence: A Step-by-Step Guide

Explicit Formula for Arithmetic Sequence

The explicit formula for an arithmetic sequence is used to find any term in the sequence by using the position of the term

The explicit formula for an arithmetic sequence is used to find any term in the sequence by using the position of the term. An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant.

The explicit formula can be written as:

𝑎𝑛 = 𝑎₁ + (𝑛−1)𝑑

Where:
– 𝑎𝑛 is the term that you want to find.
– 𝑎₁ is the first term in the sequence.
– 𝑑 is the common difference between the terms.
– 𝑛 is the position or term number in the sequence.

To use the explicit formula, you need to know the value of 𝑎₁ (the first term), 𝑛 (the position of the term), and 𝑑 (the common difference).

Let’s consider an example to demonstrate the use of the explicit formula:

Example:
Find the 7th term of an arithmetic sequence if the first term is 3 and the common difference is 4.

Solution:
Using the explicit formula, we can substitute the given values into the formula:

𝑎𝑛 = 𝑎₁ + (𝑛−1)𝑑

𝑎₇ = 3 + (7−1)4

Now, simplify the expression:

𝑎₇ = 3 + 6×4

𝑎₇ = 3 + 24

𝑎₇ = 27

So, the 7th term of the arithmetic sequence is 27.

It is important to note that the explicit formula can also be used to find the common difference or the position of a term if other values are known in the sequence.

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