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Arithmetic Sequences Practice Problems

Find the common difference, then use a_n = a_1 + (n − 1)d. The later problems work backwards from two terms or a target value.

  1. 1.

    Find the common difference of

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    Each term is 5 more than the one before: .

  2. 2.

    Find the next term of

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    The common difference is , so the next term is .

  3. 3.

    An arithmetic sequence has and . Find .

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    .

  4. 4.

    Write the explicit formula for in the form (use n).

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    .

  5. 5.

    Find the 20th term of

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    .

  6. 6.

    An arithmetic sequence has and . Find .

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    .

  7. 7.

    Which term of is 62?

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    , so and .

  8. 8.

    In an arithmetic sequence, and . Find .

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    Five steps add 20, so . Then .

  9. 9.

    For the same sequence (, ), find .

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    .

  10. 10.

    A sequence is defined by and . Find .

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    4, 10, 16, 22, 28, so .

  11. 11.

    A theater has 22 seats in row 1 and 3 more seats in each row after that. How many seats are in row 12?

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    .

  12. 12.

    Insert four numbers between 3 and 23 so that all six form an arithmetic sequence. List the four numbers.

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    Five steps cover 20, so : 3, 7, 11, 15, 19, 23.
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Arithmetic Sequences Practice Problems

These problems follow the arithmetic sequences lesson. In every one, the same number is added to get from one term to the next.

The formula

Common mistakes to watch for

  • Using instead of . The formula is ; the first term needs no added difference.
  • Finding backwards. , the later term minus the earlier one.
  • Losing a negative difference. A decreasing sequence has .
  • Confusing it with a geometric sequence. Arithmetic sequences add the same amount; geometric ones multiply by the same amount.

Frequently Asked Questions

What is the formula for the nth term of an arithmetic sequence?+

a_n = a_1 + (n − 1)d, where a_1 is the first term and d is the common difference.

How do I find d from two terms that are not next to each other?+

Divide the change in the terms by the number of steps between them. From a_4 = 17 to a_9 = 37 is 20 over 5 steps, so d = 4.

How do I type my answers?+

Type numbers without units or commas, and fractions like 7/9. For formulas, use n and ^ for powers, such as 3n - 1 or 5*2^(n - 1).

Calculators for this topic

Arithmetic Sequence Calculator

More practice problems

Geometric Sequences Practice Problems Arithmetic Series Practice Problems Arithmetic vs Geometric Sequences Practice Problems