+216 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?
+130493 Let the first term = 2
Let the last term = 2 + 5(n-1) = 5n - 3
Sum = [ 2 + 5n -3 ] [n/2] > 100
[ 5n - 1 ] [ n ] > 200
5n^2 - n > 200
5n^2 - n - 200 > 0
Set this = 0
5n^2 - n -200 = 0
n ≈ 6.4253
n = ceiling [ 6.4253 ] = 7
The 7th term produces the scream = 5(7) - 3 = 32
2, 7, 12, 17, 22 , 27 , 32
Sum 9 21 38 60 87 119
+1952 Using the information from the problem, we can write an arithmetic sequence.
For that sequence, let's let n be the number number in the sequence. We can write the expression
2+5(n−1)
We want this number to be greater or equal to 100, so we can write the inequality
2+5(n−1)≥100
Now, we solve for n,
2+5n−5≥100−3+5n≥1005n≥103n≥20.6
Since n has to be an integer, the smallest n can be is 21.
This means that n is 21. Plugging this back in, we get
2+5(21−1)2+5(20)2+100102
So our final answer is 102
Thanks! :)
+130493 Let the first term = 2
Let the last term = 2 + 5(n-1) = 5n - 3
Sum = [ 2 + 5n -3 ] [n/2] > 100
[ 5n - 1 ] [ n ] > 200
5n^2 - n > 200
5n^2 - n - 200 > 0
Set this = 0
5n^2 - n -200 = 0
n ≈ 6.4253
n = ceiling [ 6.4253 ] = 7
The 7th term produces the scream = 5(7) - 3 = 32
2, 7, 12, 17, 22 , 27 , 32
Sum 9 21 38 60 87 119
