Math Problem Statement

What is a formula for the nth term of the given sequence?

−11,−7,−3...

Solution

To find the formula for the nnth term of the given sequence 11,7,3,-11, -7, -3, \ldots, we first need to determine the pattern or rule that defines the sequence. This sequence appears to be arithmetic, where the difference between consecutive terms is constant.

Step-by-Step Solution

  1. Identify the common difference:

    To confirm that the sequence is arithmetic, calculate the difference between consecutive terms:

    7(11)=7+11=4-7 - (-11) = -7 + 11 = 4 3(7)=3+7=4-3 - (-7) = -3 + 7 = 4

    The common difference dd is 44.

  2. Find the first term:

    The first term a1a_1 of the sequence is 11-11.

  3. Use the formula for the nth term of an arithmetic sequence:

    The formula for the nth term of an arithmetic sequence is given by:

    an=a1+(n1)da_n = a_1 + (n-1)d

    Here:

    • a1=11a_1 = -11 (the first term)
    • d=4d = 4 (the common difference)
  4. Substitute the values into the formula:

    an=11+(n1)4a_n = -11 + (n-1) \cdot 4
  5. Simplify the formula:

    an=11+4n4=4n15a_n = -11 + 4n - 4 = 4n - 15

Final Formula

The formula for the nnth term of the sequence 11,7,3,-11, -7, -3, \ldots is:

an=4n15a_n = 4n - 15

This formula allows you to find any term in the sequence by substituting the value of nn.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the formula for the sum of the first nn terms of an arithmetic sequence?
  2. How do you find the common difference in an arithmetic sequence if it is not given directly?
  3. Can you explain the difference between arithmetic and geometric sequences?
  4. How would you determine the 10th term of this sequence using the formula an=4n15a_n = 4n - 15?
  5. What changes in the formula an=4n15a_n = 4n - 15 if the common difference is changed to 66?

Tip: Always double-check the common difference in a sequence to confirm whether it is arithmetic or geometric.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences

Formulas

Arithmetic sequence nth term formula

Theorems

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Suitable Grade Level

Grades 7-9