Answers

2016-02-22T18:57:42+08:00
The sum of all multiples of 3 from 15 to 48 is 378.
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2016-02-23T02:09:15+08:00
Arithmetic sequence:  15,...48

Where:
       a₁ = 15
        a_{n} = 48
       d (common difference = 3
       n = ?

Find n:

        a_{n} = a₁ + (n-1) (d)

       48 = 15 + (n- 1) (3)

       48 = 15 + 3n - 3

       48 = 3n + 12

       3n = 48 - 12

       3n/3 = 36/3

       n = 12  The are 12 terms or multiples of 3 from 15 to 48.

Solve for the sum of the sequence (arithmetic series):
   
        S_{n}  \frac{n}{2} (a _{1} +a _{n} )
  
        S₁₂ = 12/2 (15 + 48)
  
        S₁₂ = 6 (63)
 
        S₁₂ = 378

ANSWER:  The sum of multiples of 3 from 15 to 48 is 378.

      
      

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