victormccormicke

Quinn draws two marbles from the bag without replacement. The bag initially contains 5 red marbles and 2 blue marbles.

The probability of drawing a red marble followed by another red marble is given by:

Probability(RR) = (Number of ways to draw 2 red marbles) / (Total number of ways to draw 2 marbles)

Number of ways to draw 2 red marbles = 5C2 (combinations of 5 red marbles taken 2 at a time) Total number of ways to draw 2 marbles = (5 + 2)C2 (total marbles taken 2 at a time)

So, Probability(RR) = 5C2 / (7C2)

Let's call the first term of the arithmetic sequence "a," and the common difference between consecutive terms "d."

The formula for the sum of an arithmetic sequence is given by:

Sum = (Number of terms / 2) * (First term + Last term)

In this case, we have a five-term arithmetic sequence with a sum of $100:

$100 = (5 / 2) * (a + (a + 4d))

Simplify the equation:

$100 = (5 / 2) * (2a + 4d)

Divide both sides by 5/2 to get rid of the fraction:

$100 / (5 / 2) = 2a + 4d

$100 * 2/5 = 2a + 4d

$40 = 2a + 4d

Now, we need to find the smallest possible positive integer values for "a" and "d" that satisfy this equation, where all terms are multiples of 5.