Understanding Arithmetic Sequences | The Explicit Formula and How to Use It

Explicit Formula for Arithmetic Sequence

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

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. The explicit formula for an arithmetic sequence is used to find any term in the sequence. It is also known as the nth term formula.

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 of the term we want to find
– d represents the common difference between consecutive terms

To use this formula, you need to know the value of a1 (the first term) and the value of d (the common difference). By substituting these values into the formula, you can find the desired term in the sequence.

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

Example:
Find the 10th term in the arithmetic sequence 3, 7, 11, 15, …

In this sequence, the first term a1 is 3, and the common difference d is 4 (since we are adding 4 to each term to get the next term).

Using the explicit formula:
a10 = a1 + (10 – 1)d
= 3 + (9)(4)
= 39

Therefore, the 10th term in the given arithmetic sequence is 39.

In summary, the explicit formula for an arithmetic sequence is used to find any term in the sequence by substituting the first term (a1), the position of the term (n), and the common difference (d) into the formula.

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