Question

Using an=a1rn−1, what is the 10th term in this geometric sequence? 0.2, 1, 5, 25, 125, ... f 1,953,125 g 9,765,625 h 390,625 j 78,125

Answer 1

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)