The first term of the geometric progression is b1 = 1/125, and its denominator is q = 5. Find: b4; b7

Knowing what the first term of this geometric progression is equal to b1 = 1/125 and its denominator q = 5 and using the well-known formula of the term of the geometric progression, which stands in the nth place bn = b1 * q ^ (n – 1), we find the fourth and the seventh members of this geometric sequence:

b4 = b1 * q ^ (4 – 1) = b1 * q ^ 3 = (1/125) * 5 ^ 3 = (1/5 ^ 3) * 5 ^ 3 = 5 ^ 3/5 ^ 3 = 1;

b7 = b1 * q ^ (7 – 1) = b1 * q ^ 6 = (1/125) * 5 ^ 6 = (1/5 ^ 3) * 5 ^ 6 = (1/5) ^ 3 * 5 ^ 6 = 5 ^ (- 3) / 5 ^ 6 = 5 ^ (6 – 3) = 5 ^ 3 = 125.

Answer: b4 = 1, b7 = 125.