Nth Term Of Arithmetic Sequence

In an arithmetic sequence, each term after the first is obtained by adding a common difference to the preceding term. The common difference is a constant. An arithmetic sequence can be represented using the explicit formula: a_n=a_1+(n-1)d or a_n=a+(n-1)d

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each successive number is obtained by adding a constant to the preceding number. The common difference between successive terms of an arithmetic sequence is denoted by d.

The first term of an arithmetic sequence is denoted by a, and the nth term of the sequence is given by:

a_n = a + (n – 1)d

where n is the position of the term in the sequence.

What is the nth term of an arithmetic sequence?

The nth term of an arithmetic sequence is the term in the sequence that occurs after the first n-1 terms. The first term of an arithmetic sequence is a1, and the common difference between successive terms is d. Therefore, the nth term of an arithmetic sequence is given by:

a_n = a_1 + (n-1)d

where a1 is the first term and d is the common difference.

How to find the nth term of an arithmetic sequence?

To find the nth term of an arithmetic sequence, you will need to use the following formula:

a_n = a_1 + (n – 1) * d

Where:

a_n is the nth term of the arithmetic sequence
a_1 is the first term of the arithmetic sequence
d is the common difference between successive terms of the arithmetic sequence.

For example, let’s say we have an arithmetic sequence with the first term being 5 and a common difference of 3. We can use the formula above to calculate the 5th term of this arithmetic sequence:

a_5 = 5 + (5 – 1) * 3 = 5 + 12 = 17

Now let’s try finding the 15th term:

a_15 = 5 + (15 – 1) * 3 = 5 + 42 = 47

Examples

There are many different types of sequences that occur in nature. The most common type of sequence is an arithmetic sequence. An arithmetic sequence is a list of numbers where each successive number is the previous number plus a constant. The constant is called the common difference. For example, the sequence 3, 5, 7, 9, 11 is an arithmetic sequence with a common difference of 2. The nth term of an arithmetic sequence is the term in the sequence that occurs in the nth position.

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

nth term = first term + (n – 1) × common difference

For our example above, the first term is 3 and the common difference is 2. Therefore, the third term would be 3 + (3 – 1) × 2 = 7 . This formula can be used to find any term in an arithmetic sequence.

Conclusion

In this article, we looked at the nth term of an arithmetic sequence. We saw that it is possible to calculate the nth term by using a simple formula. We also saw how to use this formula to find the sum of an arithmetic series. Finally, we looked at a few examples to see how the formula works in practice.