In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

Key Concepts

Summation Notation

Summation notation is a mathematical shorthand used to represent the sum of a sequence of terms. It typically uses the Greek letter sigma (Σ) to denote the sum, with an index of summation (often 'k') indicating the starting point and the upper limit of the summation. This notation simplifies the expression of long sums and is essential for concise mathematical communication.

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. In the given sum, the terms 5, 7, 9, 11, ..., 31 form an arithmetic sequence with a common difference of 2, which is crucial for determining the general term of the sequence for summation notation.

General Term of a Sequence

The general term of a sequence is an expression that defines the nth term of the sequence in terms of n. For an arithmetic sequence, the general term can be expressed as a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. Identifying the general term is essential for writing the sum in summation notation, as it allows for the formulation of the series in a compact form.