Math Problem Statement

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

Solution

The sequence shown in the image appears to be:

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

This looks like an arithmetic sequence where each term increases by a constant difference.

To verify this:

  1. The difference between 45\frac{4}{5} and 35\frac{3}{5} is 15\frac{1}{5}.
  2. The difference between 1 and 45\frac{4}{5} is also 15\frac{1}{5}.
  3. The difference between 65\frac{6}{5} and 1 is again 15\frac{1}{5}.

Thus, the common difference is 15\frac{1}{5}, meaning this is an arithmetic sequence. The next terms can be found by adding 15\frac{1}{5} to each subsequent term.

Would you like a detailed breakdown of how to generate the next terms, or any other clarification?


Here are five related questions you could explore:

  1. How do you find the nth term of an arithmetic sequence?
  2. What is the sum of the first n terms of this sequence?
  3. How does the common difference impact the growth of an arithmetic sequence?
  4. Can an arithmetic sequence have negative terms? How would that change the common difference?
  5. How does an arithmetic sequence compare to a geometric sequence?

Tip: In an arithmetic sequence, the common difference between consecutive terms remains constant, making it easy to predict future terms.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Common Difference

Formulas

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

Theorems

Arithmetic Sequence Theorem

Suitable Grade Level

Grades 8-10