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.