Question

Hi, please help me with this question. what is 45+46+47+ ... +53+54?

Answer 1

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

__

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

__

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

__

4) Use a spreadsheet or calculator to add them. (see attached)

Answer 2

Answer:

245

Step-by-step explanation:

1).  91 + 41 + 53 + 54 {Simplify}

2).  138 + 53 + 54 {Simplify}

3).  191 + 54 {Simplify}

4).  245 {Add}