In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a50 when a₁ = 7, d = 5.

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference (d). The general form of an arithmetic sequence can be expressed as a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and n is the term number.

First Term and Common Difference

In an arithmetic sequence, the first term (a₁) is the initial value from which the sequence starts. The common difference (d) is the fixed amount added to each term to obtain the next term. For example, if a₁ = 7 and d = 5, the sequence starts at 7 and each subsequent term increases by 5.

Finding a Specific Term

To find a specific term in an arithmetic sequence, such as a₅₀, you can use the formula a_n = a_1 + (n - 1)d. By substituting the values of a₁, d, and n into this formula, you can calculate the desired term. In this case, substituting a₁ = 7, d = 5, and n = 50 will yield the value of a₅₀.