Math Problem Statement

Type the missing numbers in this sequence: 72, 81, 90, __, 108, __.

Solution

The sequence presented in the image is: 72, 81, 90, ___, 108, ___.

To find the missing numbers, let's first identify the pattern:

  • The difference between 81 and 72 is 8172=981 - 72 = 9.
  • The difference between 90 and 81 is 9081=990 - 81 = 9.

This suggests that the sequence increases by 9 each time.

Following this pattern:

  • The next number after 90 will be 90+9=9990 + 9 = 99.
  • After 108, the next number will be 108+9=117108 + 9 = 117.

So, the complete sequence is: 72, 81, 90, 99, 108, 117.

Would you like a more detailed explanation, or do you have any questions about this sequence?

Here are 5 related questions for further practice:

  1. What is the next number after 117 if the pattern continues?
  2. How can you express this sequence using an algebraic formula?
  3. What is the common difference of an arithmetic sequence?
  4. If the starting number was 80 and the difference was 5, what would the sequence look like?
  5. How can you find the nth term of an arithmetic sequence?

Tip: In an arithmetic sequence, each term increases by a constant value known as the common difference.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence

Formulas

a_n = a_1 + (n - 1) * d

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 6-8