Mastering the Explicit Formula: How to Find Any Term in an Arithmetic Sequence

Explicit Formula for Arithmetic Sequence

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

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is often denoted by ‘d’. The explicit formula for an arithmetic sequence, also known as the nth term formula, allows us to find any term in the sequence by using its position or index.

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’ represents the first term in the sequence.
– ‘n’ represents the position or index of the term we want to find.
– ‘d’ represents the common difference between consecutive terms.

To use this formula, we need to know the value of the first term (A1), the position of the term we want to find (n), and the common difference (d). By substituting these values into the formula, we can calculate the desired term.

Let’s take an example to illustrate how to use the explicit formula for an arithmetic sequence:

Example:
Consider the arithmetic sequence with a first term of 2 and a common difference of 3. We want to find the 8th term in the sequence.

Using the explicit formula:
An = A1 + (n – 1) * d

Substituting the given values:
A8 = 2 + (8 – 1) * 3

Simplifying:
A8 = 2 + 7 * 3
A8 = 2 + 21
A8 = 23

Therefore, the 8th term in the arithmetic sequence is 23.

The explicit formula for an arithmetic sequence is a powerful tool that allows us to find any term in the sequence without calculating all the preceding terms. It provides a convenient method for solving problems related to arithmetic sequences.

More Answers: