Math Problem Statement

What is the missing number sequence -10,-6,-2,_,6,10?

Solution

The given sequence is: 10,6,2,_,6,10-10, -6, -2, \_, 6, 10.

To find the missing number, observe the pattern in the sequence. The difference between consecutive terms is:

6(10)=4,2(6)=4,6?=4,106=4.-6 - (-10) = 4, \quad -2 - (-6) = 4, \quad 6 - \text{?} = 4, \quad 10 - 6 = 4.

Each number increases by 4. So, to find the missing number, add 4 to 2-2:

2+4=2.-2 + 4 = 2.

Thus, the missing number is 2.

The complete sequence is: 10,6,2,2,6,10-10, -6, -2, 2, 6, 10.

Would you like more details on sequences or further explanation?

Related questions:

  1. What is the general formula for an arithmetic sequence?
  2. How do you find the common difference in a sequence?
  3. Can an arithmetic sequence contain negative numbers throughout?
  4. How would you find the sum of all terms in an arithmetic sequence?
  5. What happens to a sequence if the common difference is negative?

Tip:

In an arithmetic sequence, the difference between any two consecutive terms is always constant.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Patterns

Formulas

Common Difference Formula: d = a_n - a_(n-1)
Arithmetic Sequence Formula: a_n = a_1 + (n-1)d

Theorems

Arithmetic Sequences Theorem

Suitable Grade Level

Grades 6-8