Find the difference between the first and third terms of an infinitely decreasing geom.

Find the difference between the first and third terms of an infinitely decreasing geom. progression, if the sum of this progression is 9, and its denominator is (1/3)

Let’s find the first term of a given geometric progression, expressing it from the formula for the sum of the members of a geometric progression:

S = b1 / (1 – q);

b1 = S * (1 – q) = 9 * (1 – 1/3) = 9 * 2/3 = 6.

Let’s find the third term of this progression:

b3 = b1 * q ^ 2 = 6 * (1/3) ^ 2 = 2/3.

Let’s find the difference between the first and third terms of the progression:

b1 – b3 = 6 – 2/3 = 5⅓.

Answer: 5⅓.