Math Problem Statement

The n-th term of a sequence is given by 5n - 3. What is the 8th term of this sequence?

Solution

To find the 8th term of the sequence given by the formula 5n35n - 3, we substitute n=8n = 8 into the formula:

5n3=5(8)35n - 3 = 5(8) - 3

=403= 40 - 3

=37= 37

Therefore, the 8th term of this sequence is 37.

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Here are some related questions you might find interesting:

  1. What is the general formula for the sum of the first nn terms of this arithmetic sequence?
  2. How do we find the nn-th term if we are given the first few terms of a sequence?
  3. What is the 15th term of this sequence?
  4. If the sequence represents a pattern, how can we determine if it is arithmetic, geometric, or neither?
  5. How do we derive the formula for the nn-th term of an arithmetic sequence?

Tip: In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The formula for the nn-th term of an arithmetic sequence is an=a1+(n1)×da_n = a_1 + (n-1) \times d, where a1a_1 is the first term and dd is the common difference.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Sequences

Formulas

nth term formula for arithmetic sequence: a_n = 5n - 3

Theorems

Arithmetic sequence formula

Suitable Grade Level

Grades 6-8