+1839 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 100, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming and running?
+129852 By " brute force " .....
Laverne says 2 7 12 17 22 27 32
Progressive sums 9 21 38 60 87 119
Another (more mathematical ) way
First term Laverne says = 2
Let the last term she says = 2 + 5n
Sum > 100
[ 2 + (2 + 5n) ] * n / 2 > 100
[ 5n + 4 ] * n > 200
5n^2 + 4n - 200 > 0 (1) set = 0 and solve for positive n
5n^2 + 4n - 200 = 0
n = [ -4 + sqrt [ 16 + 4000] ] / 10 ≈ 5.9
≈ 5.9 is a root of 5n^2 + 4n - 200....so....the next largest integer also makes (1) true
n = 6
And the number that Laverne says is 2 + 5(6) = 32
+302 She starts at 2, so she at least needs 98 more to go.
The only number that is divisible by 5 and is the smallest number greater than 98 is 100
So Laverne sends Shirley screaming and running at 2 + 100 = 102
+129852 By " brute force " .....
Laverne says 2 7 12 17 22 27 32
Progressive sums 9 21 38 60 87 119
Another (more mathematical ) way
First term Laverne says = 2
Let the last term she says = 2 + 5n
Sum > 100
[ 2 + (2 + 5n) ] * n / 2 > 100
[ 5n + 4 ] * n > 200
5n^2 + 4n - 200 > 0 (1) set = 0 and solve for positive n
5n^2 + 4n - 200 = 0
n = [ -4 + sqrt [ 16 + 4000] ] / 10 ≈ 5.9
≈ 5.9 is a root of 5n^2 + 4n - 200....so....the next largest integer also makes (1) true
n = 6
And the number that Laverne says is 2 + 5(6) = 32
