SOLUTION: 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

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Question 1173921: 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
Found 3 solutions by ewatrrr, MathTherapy, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

arithmetic series: d = 3  5th term = 4

*a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad

a%5B5%5D=a%5B1%5D%2B%284%29%2A3

 a%5B1%5D%2B+12+=+4

     a%5B1%5D+=+-8

  a%5B15%5D=-8+%2B14%2A3+=+34

*S%5Bn%5D=%28n%28a%5B1%5D%2Ba%5Bn%5D%29%29%2F2

S%5B15%5D+=+15%28-8%2B34%29%2F2+=+15%2A13+=+highlight_green%28195%29+

   Wish You the Best in your Studies.

Answer by MathTherapy(10552) About Me  (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: matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29                           

                                   

 Sum of the 1st 15 terms of AP, or

Answer by greenestamps(13200) About Me  (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.