Math Problem Statement

Write the following series in sigma notation. 8, plus, 12, plus, 16, plus, 20, plus, 24, plus, 28 8+12+16+20+24+28

Solution

The series you provided is:

8+12+16+20+24+288 + 12 + 16 + 20 + 24 + 28

This is an arithmetic series where the first term a1=8a_1 = 8, and the common difference d=4d = 4.

To express this in sigma notation:

n=16(4n+4)\sum_{n=1}^{6} (4n + 4)

This represents the sum of the first 6 terms, where the general term 4n+44n + 4 gives each term in the series.

Would you like further details on how to construct sigma notation for arithmetic series or have any other questions?


Here are five questions related to this concept:

  1. How do you find the sum of an arithmetic series?
  2. What is the general form of an arithmetic sequence?
  3. How do you determine the number of terms in a series?
  4. Can you convert any sequence into sigma notation?
  5. What are the differences between arithmetic and geometric series?

Tip: Sigma notation is useful for representing long sums in a concise way, especially when dealing with arithmetic or geometric progressions.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Series
Sigma Notation
Sequences

Formulas

General term of an arithmetic sequence: a_n = a_1 + (n-1)d
Sum of an arithmetic series: S_n = n/2 * (a_1 + a_n)

Theorems

Arithmetic Series Formula
Sigma Notation

Suitable Grade Level

Grades 9-11