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10 August, 07:32

What is the first term of the geometric sequence presented in the table below?

n 5 7

an 176 704

Hint: an = a1 (r) n - 1, where a1 is the first term and r is the common ratio.

A. a1 = - 4

B. a1 = 11

C. a1 = 35

D. a1 = - 11

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Answers (1)
  1. 10 August, 08:45
    0
    To get the first term of the geometric sequence we proceed as follows;

    The formula for the arithmetic sequence is:

    an=ar^ (n-1)

    the 5th term is 176, thus;

    176=ar^ (5-1)

    176=ar^4 ... i

    the 7th term is 704, thus;

    704=ar^ (7-1)

    704=ar^6 ... ii

    from i

    a=176/r^4

    from ii

    a=704/r^6

    hence;

    176/r^4=704/r^6

    cross-multiplying the expression we get;

    176r^6=--704r^4

    dividing both sides by 176r^4 we get:

    r^2=4

    thus

    r=sqrt4

    r=2

    therefore the first term will be:

    a=176/r^4

    a=176/2^4

    a=11
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