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Mathematics, four units · Ages 16–17

Finding a_1 and d in Arithmetic Sequences

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Use the given terms to find the common difference (d) and the first term (a_1) for each arithmetic sequence. Write your answers in simplest form.

  1. Given a_3 = 11 and a_4 = 15. Find d and a_1.

  2. Given a_2 = 9 and a_6 = 25. Find d and a_1.

  3. Given a_4 = 22 and a_8 = 46. Find d and a_1.

  4. Given a_3 = 20 and a_7 = 8. Find d and a_1.

  5. Given a_5 = -2 and a_11 = -20. Find d and a_1.

  6. Given a_6 = 14.5 and a_10 = 22.5. Find d and a_1.

  7. In an arithmetic sequence, a_7 = 53 and a_13 = 101. Find d, a_1, and the value of a_20.

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Finding a_1 and d in Arithmetic Sequences

Answer key

  1. Given a_3 = 11 and a_4 = 15. Find d and a_1.

    d = 4, a_1 = 3

  2. Given a_2 = 9 and a_6 = 25. Find d and a_1.

    d = 4, a_1 = 5

  3. Given a_4 = 22 and a_8 = 46. Find d and a_1.

    d = 6, a_1 = 4

  4. Given a_3 = 20 and a_7 = 8. Find d and a_1.

    d = -3, a_1 = 26

  5. Given a_5 = -2 and a_11 = -20. Find d and a_1.

    d = -3, a_1 = 10

  6. Given a_6 = 14.5 and a_10 = 22.5. Find d and a_1.

    d = 2, a_1 = 4.5

  7. In an arithmetic sequence, a_7 = 53 and a_13 = 101. Find d, a_1, and the value of a_20.

    d = 8, a_1 = 5, a_20 = 157