1. ## Arithmetic Sequences

What is the sum of the first 100 terms of this sequence: 5, 11, 17, 23...?

3. ## Re: Arithmetic Sequences

I know how to calculate this but according to a site, my calculations are wrong. I did 5 + 6*99 which indicates the final term. Adding the final term to the first term 599+5 and dividing that by 2, would be the average. The number of terms as stated is 100, so the answer should be 302 * 100, but according to the site, that's not the answer, so I don't know what I did wrong here.

4. ## Re: Arithmetic Sequences

The sum of an arithmetic sequence is given by $S_n = \dfrac{n}{2}(2a + (n-1)d)$ where

• $n$ is the number of terms
• $a = U_1$ which is the first term
• $d$ is the common difference (between terms)

You are told that $n=100$ and it's not hard to see that $a=5$. Now all that's left is to find the common difference and then plug into the formula at the top of this post.

L'edit: Google Calculator gives 30,200 as a answer which is evidently the same as 302*100

5. ## Re: Arithmetic Sequences

Originally Posted by Saphira
What is the sum of the first 100 terms of this sequence: 5, 11, 17, 23...?
$5+[5+6]+[5+(2)6]+[5+(3)6]+....+[5+(99)6]$

$=(100)5+6(1+2+3+....+99)$

$=500+6[(50-49)+(50-48)+.....+50+....+(50+48)+(50+49)]$

$=500+6(99)50$

However, you are probably expected to use the general formula for summing an arithmetic series,
having recognised the series as "arithmetic"
from the constant difference between terms.

6. ## Re: Arithmetic Sequences

Originally Posted by Saphira
I know how to calculate this but according to a site, my calculations are wrong. I did 5 + 6*99 which indicates the final term. Adding the final term to the first term 599+5 and dividing that by 2, would be the average. The number of terms as stated is 100, so the answer should be 302 * 100, but according to the site, that's not the answer, so I don't know what I did wrong here.
6*99= 6(100- 1)= 600- 6= 594, not 599.

7. ## Re: Arithmetic Sequences

Originally Posted by HallsofIvy
6*99= 6(100- 1)= 600- 6= 594, not 599.
5+6*99 is the final term, which is 599.
Then Saphira is calculating the average of all the terms
by averaging the first and last terms, which are 5 and 599,
as the sum may be evaluated using

sum=(average)(number of terms).