Math Problem Statement

What is the next term of the arithmetic sequence? [-2,3,8,13,18,]

Solution

In an arithmetic sequence, the difference between consecutive terms is constant. This difference is called the common difference (dd).

Step 1: Find the Common Difference

d=3(2)=5d = 3 - (-2) = 5 d=83=5d = 8 - 3 = 5 d=138=5d = 13 - 8 = 5 d=1813=5d = 18 - 13 = 5 Since the common difference is 5, the sequence follows the pattern of adding 5 to each term.

Step 2: Find the Next Term

Next term=18+5=23\text{Next term} = 18 + 5 = 23

Answer:

23\mathbf{23}

Would you like a general formula for the sequence? Let me know if you have any questions!


Related Questions:

  1. What is the general formula for the given arithmetic sequence?
  2. What is the 10th term of the sequence?
  3. How do you find the sum of the first 20 terms of this sequence?
  4. If the sequence continues, which term will be equal to 98?
  5. How do you determine if a given number is part of the sequence?

Tip:

To find any term in an arithmetic sequence, use the formula:
an=a1+(n1)da_n = a_1 + (n-1) d
where a1a_1 is the first term, dd is the common difference, and nn is the term number.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequence
Common Difference
Sequence Patterns

Formulas

a_n = a_1 + (n-1) d

Theorems

Arithmetic Sequence Theorem

Suitable Grade Level

Grades 6-8