math-algebra

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14. The last term of an arithmetic sequence is 207, the common difference is 3, and the number of terms is 14. What is the first term of the sequence?:
A. 165

B. 171

C. 249

D. 168

Please explain. thanks

  • math-algebra -

    Subtract the difference from the last term 13 times, since the last term is the 14th number. Can you think of a faster way to do this?

    I hope this helps. Thanks for asking.

  • math-algebra -

    The last term of an arithmetic sequence is 207, the common difference is 3, and the number of terms is 14. What is the first term of the sequence?:
    A. 165

    B. 171

    C. 249

    D. 168

    Please explain. thanks

    The last, or nth, term of an arithmetic progression is defined by L = a + (n - 1)d where L = the last term, a = the first term, n = the number of terms and d = the common difference.

    Therefore, 207 = a + (14 - 1)3
    ...............= a + 39

    Therefore, a = 207 - 3396 = 168.

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