anonymous
  • anonymous
What is the average of all of the integers from 13 to 37?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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apoorvk
  • apoorvk
sum them all up with the AP sum formula... then divide by the no. of nos. to get the mea, or the 'avg.'
experimentX
  • experimentX
(13+37)/2 .. if it is symmetric on some no
experimentX
  • experimentX
I thought @Tributized might be right .. if you can constrct (24+25+26)/3 = 25

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More answers

anonymous
  • anonymous
i deleted it because u were teaching the asker ._. i don't wanna give the answer yet lol
experimentX
  • experimentX
(23+24+25+26+27)/5 = 25 (13+ ... +23+24+25+26+27+ ,,,,, 37)/(37-13) = 25
experimentX
  • experimentX
no .. i just came up with a hunch .. i haven't calculated yet ... this is just interesting ... to predict result without calculating
anonymous
  • anonymous
I see
anonymous
  • anonymous
oh ok. so the answer is 25. :D
experimentX
  • experimentX
seriously, i haven't checked it yet .... just a prediction
experimentX
  • experimentX
everybody is giving me medals .. guess i was right or what :D
TuringTest
  • TuringTest
\[\frac12[\sum_{i=1}^{37}i-\sum_{i=1}^{12}i]\]eh? may not be the most efficient way
anonymous
  • anonymous
yep ur right. since im right :D
anonymous
  • anonymous
The average (or mean) is the same as the median with a series of numbers which differentiate from each other by the same number (in this case, 1)
anonymous
  • anonymous
(13+37)/2 = (14+36)/2 = (15+35)/2 = ... = (24+26)/2 = 25/1 = 25, you only needed to calculate (13+37)/2 =25. The same is true for any sum of consecutive integers.
anonymous
  • anonymous
Turing, why dividing by 2?
TuringTest
  • TuringTest
oops divide by 37-12
TuringTest
  • TuringTest
right?
anonymous
  • anonymous
the sum is \[\S_{n}=\frac{n}{2}(a_{1}+a_{n})\] the average would be \[\frac{\S_{n}}{a_{n}-a_{1}}=\frac{\frac{a_{n}-a_{1}}{2}(a_{1}+a_{n})}{a_{n}-a_{1}}=\frac{\frac{37-13}{2}(37+13)}{37-13}=\frac{37+13}{2}\]
anonymous
  • anonymous
13 through 37 is the same as 12(25) = 300 ( there are 25 numbers to add ) add to this the numbers 1 through 25 The formula for this is: (1/2) x 25 x 26 = 325 300 + 325 = 625 625/25 = 25
anonymous
  • anonymous
I did this \[ (37 \times 38/2 - 12 \times 13/2)/(37-12) = 25\]
anonymous
  • anonymous
yeah that's easier lol
TuringTest
  • TuringTest
oh jeez, I added in my calculator at least that earlier formula is right then with the modification mentioned by FFM\[\frac1{25}[\sum_{i=1}^{37}i-\sum_{i=1}^{12}i]\]

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