Generate an abstract representation of a mathematical problem involving the summation of multiples of six between the numbers 6 and 999. This thought-provoking scene should reflect the contrasting numbers, with elements representing both the student's answer of 83166 and the answer key's solution of 82665. Visualize the process of using numerical formulas to solve the problem but ensure the artwork contains no text.

The sum of multiples of 6 between 6 & 999?

I got 83166, but my answer key says 82665.. Is my answer wrong? I used the term formula to find 166 terms multiples of 6, and then the sum formula to get 83166.

So you have 6 + 12 + 18 + ... + 996

this is an AS where a = 6, d = 6
so 996 = 6 + (n-1)(6)
996 = 6 + 6n - 6
6n = 996
n = 166 , you are right so far

sum(166) = 83(first + last)
= 83(6 + 996) = 83166 , you had that too

or using the more standard sum formula
S(n) = (n/2)(2a + (n-1)d)
= (166/2)(12 + 165(6) )
= 83166

The only thing I see is they said "between",
so exclude the first term but keep last term
83166 - 6 = 83160

check on that, now we only have 165 terms
sum = (165/2)(12 + 996) = 83160 , as above

Oh, math can be quite tricky sometimes! It seems like you've made a tiny little mistake. The correct sum of multiples of 6 between 6 and 999 is actually 82665. But hey, don't be too hard on yourself - maybe you just accidentally added a clown nose to one of the numbers!

fkjnisk

To solve this problem, we need to find the sum of multiples of 6 between 6 and 999. Let's break it down step by step to double-check your answer:

1. First, calculate the number of terms: To find the number of terms in a sequence of multiples, we can use the formula: number of terms = (last term - first term) / common difference + 1. In this case, the first term is 6, the last term is 999, and the common difference is 6. Plugging these values into the formula, we get: (999 - 6) / 6 + 1 = 166 + 1 = 167.

2. Next, calculate the sum: To find the sum of an arithmetic sequence, we can use the formula: sum = (number of terms / 2) * (first term + last term). Plugging in the values we found, we have: sum = (167 / 2) * (6 + 999) = 83.5 * 1005 = 83767.5.

Now, let's compare the result with your answer:
- Your answer: 83166
- Correct answer: 83767.5

It seems that your calculated sum of 83166 is slightly different from the correct answer of 83767.5. This discrepancy might be due to a rounding error or missing a fraction in the calculation. Therefore, your answer is indeed incorrect, and the correct sum of the multiples of 6 between 6 and 999 is 83767.5, rounded to 82665 according to your answer key.

Your method is correct but you have to use n=165 and not 166, because it says between 6 and 999.

The sequence will be 6,12,18.....996
With t1=6, tn=996 and n=165.
Use the summation formula,
You will get Sn=82665.