Find the 1st term of a geometric progression (bn) if b7 = 0.005, q = 1/2

As we well know from school geometry programs, any term of such a progression can be calculated using the following formula:

bn = b1 * q ^ (n – 1).

That is, the first term of such a progression can be calculated through:

b1 = bn: q ^ (n – 1).

Let us determine from what number our geometric progression will begin, when from the condition of the task we know that the number 0.005 is in seventh place in it, while its denominator is 1/2:

0.005: 1/2 ^ (7 – 1) = 0.005: 1/64 = 0.32.

Answer: b1 = 0.32.