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# Algebra

-2
3
2
+153

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?

Jun 14, 2024

#2
+129712
+1

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

Jun 15, 2024

#1
+1204
+1

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

\(2+5(n-1) \geq 100\)

Now, we solve for n,

\(2+5n-5 \geq 100\\ -3+5n \geq 100\\ 5n \geq 103\\ n \geq 20.6\)

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

\(2+5(21-1)\\ 2+5(20)\\ 2+100\\ 102\)

So our final answer is 102

Thanks! :)

Jun 14, 2024
#2
+129712
+1

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

CPhill Jun 15, 2024