Tuesday, September 8, 2015

High School Math Solutions – Algebra Calculator, Sequences

When dealing with simpler sequences, we can look at the sequence and get a feel for what the next term or the rule is.  However, not all sequences are nice like those. Finding the rule of a sequence can be difficult if you don’t know where to begin. We will focus on arithmetic and geometric sequences, which will make finding the rule, term, and sum of terms very easy.

Arithmetic Sequence:
  • A sequence where the difference between the consecutive terms is constant
  • Finding the nth term: a_n=a_1+(n-1)d
  • Find the sum of n terms: S_n=\frac{n(a_1+a_n)}{2}

Geometric Sequence:
  • A sequence where each term is multiplied the previous term by a constant
  • Finding the nth term: a_n=a_0\cdot r^{n-1}
  • Find the sum of n terms: S_n=\frac{a_1(1-r^n)}{1-r}

Here we will go through a problem involving an arithmetic sequence step by step (click here):

1. See if you can see a pattern
Find the next 3 terms of the following sequence: 3,11,19,27,35,...
We can see that difference in each term is 8. 
2. Plug terms into the formula
3. Compute terms

We will now go through a problem involving a geometric sequence step by step (click here):
Find the 7th term of the following sequence:  \frac{2}{9},\frac{2}{7},2,6,18
1. Check to see if the ratio is constant

2. Plug terms into formula
a_n=\frac{2}{9}\cdot 3^(n-1)
3. Compute term
a_7=\frac{2}{9}\cdot 3^6=162

Here’s an example where you have to find the sum of terms (click here):

Arithmetic and geometric series aren’t very hard. Just memorize the formulas and it should be pretty easy.

Until next time,


  1. This comment has been removed by the author.

  2. Thanks for sharing.I found a lot of interesting information here. A really good post, very thankful and hopeful that you will write many more posts like this one.



  3. Wow actually i loved your blog man..Thanks for sharing awesome content..

    Online notepad++
    psiphon pro


  4. Hi after reading your blog I have finally found some knowledge which
    I was looking for so long for that reason Thanks..
    facetime for android

  5. From this page you will get some info on how to write exceptionally good essay. I think that you should do it as soon as possible

  6. So as to ace arithmetic you need to ace the polynomial math ideas. Get familiar with the nuts and bolts of polynomial math effectively, proceed onward to progressively convoluted issues, learn them. At that point push ahead to significantly progressively complex issues. Etc. root finder

  7. We offer research papers writing help that focuses on satisfying the academic needs of students at any time they need help and also affordable custom essay writing help services.

  8. Nicely written and great info, I really thank you for sharing it. Looking forward read more, great article. I value the post, really looking forward to read more.so keep posting.
    If you have a Quickbooks Desktop and you are thinking about shifting to QBO then you should take assistance from Quickbook Customer Servic for better migration. They will assist you to import your files completely without losing data.

  9. Currently it looks like article is the top blogging platform available right now.

  10. thank you.

    โปรโมชั่นGclub ของทางทีมงานตอนนี้แจกฟรีโบนัส 50%
    เพียงแค่คุณสมัคร สล็อตออนไลน์ กับทางทีมงานของเราเพียงเท่านั้น
    สมัครสล็อตออนไลน์ >>> Goldenslot
    สนใจร่วมสนุกกับ คาสิโนออนไลน์ คลิ๊กได้เลย
    มีทั้งคาสิโนออนไลน์ หวยออนไลน์ ฟุตบอลออนไลน์ สล็อตออนไลน์ และอื่นๆอีกมากมาย

  11. great article, I was very impressed about it, wish you would have stayed next share
    fireboy and watergirl 8

  12. It affects human blood cells According to the outcomes performed by some vape juice scientists, the nine constitute of the vape juice taste have numerous impacts on endothermic cells. The majority of the damaged cells play a major duty in all blood tasks. worldvaping