Calculating the Sum of 25 Terms of an Arithmetic Sequence: An SEO-Optimized Article

Are you looking for an efficient way to find the sum of a specific number of terms in an arithmetic sequence? In this article, we will walk you through the process of finding the sum of the first 25 terms of the given arithmetic sequence 1/9, 2/9, 3/9, ..., 25/9. This topic is particularly useful for students studying mathematics, as well as for professionals working in fields that require numerical analysis. By the end of this article, you will understand the formulae and the steps required to solve such problems.

Understanding the Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant, known as the common difference, to the previous term. In this specific sequence, the first term a 1/9 and the common difference d 1/9.

The Sum Formula for an Arithmetic Sequence

The sum of the first n terms of an arithmetic sequence can be found using the formula:

Sn (n/2) × (2a (n - 1) × d)

Identifying the First Term and Common Difference

Let's begin by identifying our known values:

The first term, a 1/9 The common difference, d 1/9 The number of terms, n 25

Calculating the Last Term (25th Term)

We can find the 25th term of the sequence using the formula for the n-th term of an arithmetic sequence:

an a (n - 1) × d

Substituting the known values:

a25 1/9 (25 - 1) × 1/9

a25 1/9 24 × 1/9

a25 (1 24) / 9 25/9

Calculating the Sum of the First 25 Terms

Now that we know the first and last terms, we can use the sum formula:

S25 (25/2) × (1/9 25/9)

S25 (25/2) × (26/9)

S25 (25 × 26) / (2 × 9) 650 / 18 325 / 9

Conclusion

The sum of the first 25 terms of the given arithmetic sequence is 325/9. This method can be applied to other arithmetic sequences following the same pattern, making it a versatile tool for solving similar problems.

Keywords: arithmetic sequence, sum of terms, formula