Math Problem Statement

Answer the question

Write the following arithmetic series in sigma notation: 8 + 16 + 24 + ... + 75

Solution

The question asks to write the arithmetic series given in sigma notation, and the series is:

8+16+24+32++758 + 16 + 24 + 32 + \ldots + 75

Now, let's find the correct sigma notation representation. The series is arithmetic with the following characteristics:

  1. First term a=8a = 8
  2. Common difference d=8d = 8
  3. The last term is 7575

The general form of an arithmetic sequence is:

an=a+(n1)da_n = a + (n - 1) \cdot d

To find the total number of terms nn, use the equation for the nn-th term:

75=8+(n1)875 = 8 + (n - 1) \cdot 8

Solving for nn:

67 = (n - 1) \cdot 8 \\ n - 1 = \frac{67}{8} = 8.375 \quad \text{(invalid)}$$ It seems I made a mistake in interpreting the terms. Let me correct it.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Sigma Notation
Series

Formulas

General form of an arithmetic sequence: a_n = a + (n - 1) * d
Sigma notation for arithmetic series: Σ from n = 1 to n of a + (n - 1) * d

Theorems

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Suitable Grade Level

Grades 9-12