Understanding Arithmetic Sequences | Definition, Calculation, and Applications

Arithmetic Sequences

Arithmetic sequences are sequences of numbers in which the difference between any two consecutive terms is constant

Arithmetic sequences are sequences of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the “common difference” denoted by the letter “d”.

Let’s take an example to better understand arithmetic sequences. Consider the following sequence: 3, 6, 9, 12, 15, 18, …

In this sequence, the common difference, ‘d’, is 3. This means that each term is obtained by adding 3 to the previous term. For example, 6 = 3 + 3, 9 = 6 + 3, and so on.

To find the nth term of an arithmetic sequence, we can use the general formula:

an = a1 + (n – 1)d

Here, ‘an’ represents the nth term, ‘a1’ is the first term, ‘n’ is the position of the term in the sequence, and ‘d’ is the common difference.

For example, let’s find the 10th term of the arithmetic sequence mentioned earlier. We know that the first term, a1, is 3 and the common difference, d, is 3. Plugging these values into the formula, we have:

a10 = 3 + (10 – 1) * 3
= 3 + 9 * 3
= 3 + 27
= 30

Therefore, the 10th term of the sequence is 30.

Arithmetic sequences are useful in various mathematical applications, such as calculating the growth of investments, predicting patterns in numbers, and solving problems involving uniform change.

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