SOLUTION: The sum of an arithmetic series is 100 times the value of its first term, while the last term is 9 times the first term. Calculate the number of terms in the series if the first te

Question 1134943: The sum of an arithmetic series is 100 times the value of its first term, while the last term is 9 times the first term. Calculate the number of terms in the series if the first term is not equal to zero.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Formula for sum:

----------------------------------

---------------------

-------------------

29 terms
---------------
check:

I used instead of
That's the error, I think. Definitely get
a 2nd opinion on this.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The other tutor mistakenly used the formulas for geometric series instead of arithmetic series....

The last term is 9 times the first term, so we can call the first and last terms a and 9a.

The average of the terms in an arithmetic sequence is the average of the first and last terms, so the average of the terms in the sequence is 5a.

The sum of the terms of an arithmetic series is the average of the terms, multiplied by the number of terms. Since the sum of the terms is 100 times the first term, the number of terms n can be found with

There are 20 terms in the series.
RELATED QUESTIONS
In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is... (answered by MathTherapy)
In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is... (answered by MathLover1,MathTherapy)
Find the sum of the series 1+3.5+6+8.5+......+101 Find the sum of the first 23 term of... (answered by Edwin McCravy,ikleyn)
The first term and the last term of an arithmetic series is 5 and 61 respectively while... (answered by ikleyn)
in an arithmetic series, the second to last term is three times the fifth term, the sum... (answered by Edwin McCravy)
The first term of an arithmetic series is 2. The 10th term is 61. Calculate s10. (answered by reviewermath)
Find the sum of the first 30 terms of an arithmetic series if the 1st term is 5 and the... (answered by ikleyn)
In a geometric series, the 9th term is equal to 8 times the 6th term, while the sum of... (answered by robertb)
the first term of an arithmetic sequence is -14 while the sum of the first 20 term is... (answered by Finavon)