Hi, please help me with this question. what is 45+46+47+ ... +53+54?
2 answers:
9514 1404 393
Answer:
495
Step-by-step explanation:
There are several ways to figure this:
1) Multiply the average value by the number of numbers. The average number in an arithmetic sequence is the average of the first and last numbers in the sequence.
average = (54+45)/2 = 49.5
number of numbers = 54 -45 +1 = 10
Total = 49.5 · 10 = 495
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2) Add the numbers pairwise. It works best to work toward the middle from the ends:
45 +54 = 99
46 +53 = 99
47 +52 = 99
48 +51 = 99
49 +50 = 99
Total = 5 · 99 = 495
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3) Subtract the sum of numbers to 44 from the sum of numbers to 54.
The sum of numbers 1 to n is (n)(n+1)/2.
(54)(55)/2 -(44)(45)/2 = (27)(55) -(22)(45) = 1485 -990 = 495
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4) Use a spreadsheet or calculator to add them. (see attached)
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