Math Problem Statement

Write the following series in sigma notation. 9, plus, 12, plus, 15, plus, 18, plus, 21 9+12+15+18+21

Solution

The given series is an arithmetic series where the first term a=9a = 9, the common difference d=3d = 3, and there are 5 terms.

In sigma notation, an arithmetic series can be written as:

n=1N(a+(n1)d)\sum_{n=1}^{N} \left( a + (n-1) \cdot d \right)

For this specific series, we have:

  • a=9a = 9
  • d=3d = 3
  • N=5N = 5

Thus, the sigma notation for the series is:

n=15(9+(n1)3)\sum_{n=1}^{5} \left( 9 + (n-1) \cdot 3 \right)

Would you like more details on how this notation works?

Here are 5 related questions you might find interesting:

  1. How do you derive the sum of an arithmetic series?
  2. What is the general formula for the sum of an arithmetic series?
  3. How would you write a geometric series in sigma notation?
  4. Can you find the sum of the given arithmetic series?
  5. How does sigma notation differ for infinite series?

Tip: In sigma notation, understanding the limits of summation (i.e., the range of nn) is key to interpreting the series accurately.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Series
Sigma Notation
Sequences

Formulas

\sum_{n=1}^{N} \left( a + (n-1) \cdot d \right)

Theorems

Arithmetic Series Formula

Suitable Grade Level

Grades 8-10