Math Problem Statement

The nth term of a sequence is given by 8n. Complete the table with the first three terms of the sequence.

Solution

The problem in the image states that the nth term of a sequence is given by the formula 8n8n, and you are asked to complete the table for the first three terms of the sequence.

Here’s how to calculate the first three terms using the formula 8n8n:

  1. When n=1n = 1: 8n=8×1=88n = 8 \times 1 = 8

  2. When n=2n = 2: 8n=8×2=168n = 8 \times 2 = 16

  3. When n=3n = 3: 8n=8×3=248n = 8 \times 3 = 24

Completed Table:

  • Position n=1n = 1, Term 8n=88n = 8
  • Position n=2n = 2, Term 8n=168n = 16
  • Position n=3n = 3, Term 8n=248n = 24

Let me know if you would like further explanations or have any questions!

Here are 5 related questions:

  1. What would be the term when n=4n = 4 using the same formula?
  2. Can you find the 10th term of the sequence?
  3. What is the general form of an arithmetic sequence, and how does this one fit that pattern?
  4. How would the sequence change if the formula was 8n+18n + 1 instead of 8n8n?
  5. What type of sequence is generated by this formula? Is it arithmetic, geometric, or another type?

Tip: In an arithmetic sequence, the difference between consecutive terms remains constant. In this case, the difference between terms is 88.

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Math Problem Analysis

Mathematical Concepts

Sequences
Arithmetic sequences
Algebra

Formulas

nth term of a sequence = 8n

Theorems

Arithmetic sequences theorem (common difference is constant)

Suitable Grade Level

Grades 6-8