math-algebra

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

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  1. 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.

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  2. 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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