Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming and running?
1. Find the formula for the sum of an arithmetic series:
The sum of an arithmetic series can be found using the formula:
Sum = (n/2) * (first term + last term)
where:
n = number of terms
first term = 2
last term = 2 + 5(n-1) = 5n - 3
2. Set up the inequality:
We want to find the 'n' where the sum exceeds 1000:
(n/2) * (2 + 5n - 3) > 1000
(n/2) * (5n - 1) > 1000
5n^2 - n > 1000
5n^2 - n - 1000 > 0
3. Solve the quadratic inequality:
Use the quadratic formula to find the roots of 5n^2 - n - 1000 = 0
n = [1 ± √(1 + 4 * 5 * 1000)] / (2 * 5)
n ≈ 28.3 or n ≈ -28.2
Since 'n' represents the number of terms, it must be positive.
Therefore, n > 28.3
4. Find the last number Laverne says:
Last term = 5n - 3
Since n > 28.3, the smallest integer value for 'n' is 29.
Last term = 5 * 29 - 3 = 142
Answer:
Laverne says the number 142 that sends Shirley screaming and running.