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Using the formula [tex]a_n = a_1 \cdot r^{n-1}[/tex], what is the 10th term in this geometric sequence: 0.2, 1, 5, 25, 125, ...?

A. 1,953,125
B. 9,765,625
C. 390,625
D. 78,125

Answer :

Use the formula a(n) = a(1)*r^(n-1), where r is the common factor and n is the counter.

The first term, a(1), of 0.2, 1, 5, 25, 125, ... is obviously 0.2. Note that multiplying 0.2 by 5 gives us 1; mult. 5 by 5 gives us 25, etc., so the common factor r is 5.

Thus, a(n) = a(1)*r^(n-1) becomes a(n) = 0.2*(5)^(n-1), and

a(10) = 0.2*(5)^(10-1), or 0.2*5^9, or 0.2(1953125), or 390625 (answer)

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