Math Problem Statement

find the pattern what numbers come text, 61 54 47 40 33

Solution

The sequence provided is: 61, 54, 47, 40, 33.

Let's analyze the pattern by finding the differences between consecutive terms:

  1. 5461=754 - 61 = -7
  2. 4754=747 - 54 = -7
  3. 4047=740 - 47 = -7
  4. 3340=733 - 40 = -7

The difference between each consecutive term is consistently 7-7. This indicates that the sequence is an arithmetic sequence with a common difference of 7-7.

Next number:
To find the next number in the sequence, subtract 7 from the last number, 33:

337=2633 - 7 = 26

So, the next number in the sequence is 26.

Would you like more details or have any questions about this pattern?


Here are five related questions to consider:

  1. What is the 10th term of this sequence?
  2. How can you express the general term of this arithmetic sequence using a formula?
  3. How would the sequence behave if you added 2 to each term?
  4. What is the sum of the first 15 terms of this sequence?
  5. How does this sequence compare to one with a common difference of 10-10?

Tip: In an arithmetic sequence, the formula for the nnth term 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

Arithmetic Sequences

Formulas

Arithmetic sequence formula: a_n = a_1 + (n-1) * d

Theorems

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Suitable Grade Level

Grades 7-9