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1. What is the tenth term of the geometric sequence whose first term (a1) is 16 and the common ratio (r) is –½?

2. Given the terms a10 = 3 / 512 and
a15 = 3 / 16384 of a geometric sequence, find the exact value of the first term of the sequence.

  • Math -

    term(n) = ar^(n-1)
    term(10) = 16(-1/2)^9
    = 16(-1/512)
    = - 1/32

    ar^9 = 3/512
    ar^14 = 3/16384
    divide the 2nd by the first
    r^5 = 1/32
    r = 1/2
    back into the first

    a(1/2)^9 = 3/512
    a(1/512) = 3/512
    a = 3(512)/512 = 3

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