Math Problem Statement

What is the next term in the sequence below?

What is the next term in the sequence below? 3/5, 4/5, 1, 6/5, ...

Solution

The given sequence starts as follows:

35,45,1,65,\frac{3}{5}, \frac{4}{5}, 1, \frac{6}{5}, \dots

Let's analyze this sequence:

  • The first term is 35\frac{3}{5}.
  • The second term is 45\frac{4}{5}.
  • The third term is 1=551 = \frac{5}{5}.
  • The fourth term is 65\frac{6}{5}.

The pattern suggests that each term increases by 15\frac{1}{5}. Therefore, the next term after 65\frac{6}{5} would be:

65+15=75\frac{6}{5} + \frac{1}{5} = \frac{7}{5}

Thus, the next term in the sequence is 75\frac{7}{5}.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:

  1. What type of sequence is this, arithmetic or geometric?
  2. How do you find the nth term in an arithmetic sequence?
  3. What is the general form of an arithmetic progression?
  4. Can this sequence be modeled by a linear equation?
  5. How would the sequence change if the increment were 25\frac{2}{5}?

Tip: In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. Identifying this difference is key to predicting future terms.

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Math Problem Analysis

Mathematical Concepts

Sequences
Arithmetic Progression

Formulas

nth term of an arithmetic sequence: a_n = a_1 + (n-1)d

Theorems

Arithmetic Sequence Theorem

Suitable Grade Level

Grades 6-8