Hi,

arithmetic series: d = 3  5th term = 4

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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
 Determine the sum of the 15 terms of the arithmetic series where the 5th term is 4 and consecutive terms increase by 3. 

A) 195

B) 285

C) 182

D) 169

With the 5th term being 4, we get:   

     Formula for the sum of an AP:                            

                                   

 Sum of the 1st 15 terms of AP, or  

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


Note: Both formal algebraic solutions from other tutors are fine; but there is a faster path to the answer.


The sum of 15 terms of an arithmetic series is 15 times the middle term.


In a series with 15 terms, the middle term is the 8th term.


With 5th term 4 and common difference 3, the 8th term is 4+3(3) = 4+9 = 13.


ANSWER: The sum is 15(13) = 195.


 

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