The first term of the geometric progression is 10% less than the second.

The first term of the geometric progression is 10% less than the second. How many percent is the first term of the progression less than the third?

Let b2 be the second term of this geometric progression.

The problem statement says that the first term of this geometric progression is 10% less than the second term, therefore, the first term of this progression is b2 – (10/100) * b2 = b2 – (1/10) * b2 = b2 – 0.1 * b2 = 0.9 * b2.

Find the denominator q of this geometric progression:

q = b2 / (0.9 * b2) = 1 / 0.9 = 10/9.

We find the third term b3 of this geometric progression:

b3 = b2 * q = (10/9) * b2.

Therefore, the first term of the progression is less than the third by:

100 * ((10/9) * b2 – 0.9 * b2) / ((10/9) * b2) = 100 * (10/9 – 9/10) * b2 / ((10/9) * b2) = 100 * (19/90) * 9/10 = 19%.

Answer: the first term of the progression is 19% less than the third.