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# Algebra

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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?

Jul 23, 2024

#1
+1790
+1

We can set variables to solve this question.

Let's let the first term be 2

This means that the last term \( 2 + 5(n-1)  =  5n - 3\)

The sum is  \([ 2 + 5n -3 ] [n/2]  > 100\)

\([ 5n - 1 ] [ n ] > 200 \\ 5n^2 - n > 200 \\ 5n^2  - n - 200 > 0 \)

Since we want the largest possible value, set this to equal 0. We have

\(5n^2 - n -200 =  0 \\ n ≈ 6.4253 \)

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

Thus, the final answer is 32.

Thanks! :)

Jul 23, 2024
edited by NotThatSmart  Jul 23, 2024

#1
+1790
+1

We can set variables to solve this question.

Let's let the first term be 2

This means that the last term \( 2 + 5(n-1)  =  5n - 3\)

The sum is  \([ 2 + 5n -3 ] [n/2]  > 100\)

\([ 5n - 1 ] [ n ] > 200 \\ 5n^2 - n > 200 \\ 5n^2  - n - 200 > 0 \)

Since we want the largest possible value, set this to equal 0. We have

\(5n^2 - n -200 =  0 \\ n ≈ 6.4253 \)

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

Thus, the final answer is 32.

Thanks! :)

NotThatSmart Jul 23, 2024
edited by NotThatSmart  Jul 23, 2024