SOLUTION: Question: In an arithmetic series of 50 terms, the 17th term is 53 and the 28th term is 86. Find the sum of the series. Problem: I've gone through all the steps but I ended up w

Question 662461: Question: In an arithmetic series of 50 terms, the 17th term is 53 and the 28th term is 86. Find the sum of the series.
Problem: I've gone through all the steps but I ended up with a different answer than what's in the back of my textbook. I'm going to type everything thing I did below, and hopefully someone can tell me where I messed up. I used \ when referring to division and / when referring to a fraction.
t17=53
t28=86
tn=a+(n-1)d
53=a+(17-1)d
53=a+16d
a=53-16d
Sn=n\2(2a+(n-1)d)
86=28/2(2a+(28-1)d)
86=14(2a+27d)
86=14(2(53-16d)+27d)
6/1/7=2(53-16d)+27d
6/1/7=106-32d+27d
-99/6/7=5d
-19/34/35=d
a=53-16(-19/34/35)
a=53-320
a=-267
Sn=n\2(2a+(n-1)d)
Sn= 50\2(2(-267)+(50-1)-19/34/35)
Sn=25(-534+(49)-19/34/34)
Sn=25(-1512/3/5)
Sn=-37815
The answer im the back of my textbook says it's suppose to be 3925
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The first part of your work is right.
term number is -->
term number is
--> <-->
You were on your way to finding and .
You just needed to use more data to get and .

Next, you misinterpreted "the 28th term is 86" (or maybe lost track of your planned steps)
You wrote , the formula for sum of the first terms,
followed by as if the sum of the first 28 terms was 86.
You knew that the next step would require using that formula for the sum,
but lost track, and skipped a step.

At that point, a bunch of people would write some of this:
term number is -->
term number is
-->
Then, they would use , along with to find and .
They would write the system
and would solve it to get and .

RANT:
I may write all that to go with the flow, and please a teacher,
but I prefer to use definitions, logic and 5th grader reasoning (if possible),
trying to always understand the meaning of my calculations,
rather than using formulas.
I look at it the fifth grader way:
Going from the 17th to the 28th term, we are adding from one term to the next,
and we do that times,
so the difference between the 17th and the 28th terms must be times .
The difference is , so I divide to get
Then, since you gave me ,
I use it to get --> --> .

THE SUM:

--> --> --> --> .
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