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Name the next four terms of each arithmetic sequence.

5,9,13, ...
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1 answer

To find the next four terms of the arithmetic sequence 5, 9, 13, ..., we first need to determine the common difference.

  1. Identifying the Common Difference:

    • The first term is \( a_1 = 5 \).
    • The second term is \( a_2 = 9 \).
    • The third term is \( a_3 = 13 \).

    To find the common difference \( d \): \[ d = a_2 - a_1 = 9 - 5 = 4 \] \[ d = a_3 - a_2 = 13 - 9 = 4 \] The common difference \( d \) is \( 4 \).

  2. Finding the Next Four Terms: Now we can find the next terms in the sequence by adding the common difference \( d \) to the last known term.

    • Fourth term (\( a_4 \)): \[ a_4 = a_3 + d = 13 + 4 = 17 \]

    • Fifth term (\( a_5 \)): \[ a_5 = a_4 + d = 17 + 4 = 21 \]

    • Sixth term (\( a_6 \)): \[ a_6 = a_5 + d = 21 + 4 = 25 \]

    • Seventh term (\( a_7 \)): \[ a_7 = a_6 + d = 25 + 4 = 29 \]

  3. Final Listing of Terms: The next four terms in the sequence are: \[ 17, 21, 25, 29 \]

So the final answer is: 17, 21, 25, 29.