# Arithmetic Progression

During our elementary days, our teachers told us to count by 1’s(1,2,3..), by 2’s(2,4,6…), by 3’s(3,6,9..). Without our knowledge, we are creating a series called arithmetic progression. This series is easy to understand because if you are not sure you can enumerate the elements if you forgot the formula.

Nth term of arithmetic progression;

Given that the series has first term and common difference of r

nth term formula

1^{st} term

2^{nd} term

3^{rd} term

4^{th} term

5^{th} term

Observe the pattern above about the nth term and the coefficient of r. We can tell that the coefficient of r is 1 less than the coefficient of the nth term. We can create a formula by looking at that pattern.

**Formula:**

Let – nth term, – 1^{st} term, – common difference

**Worked Problem 1:**

Give the 2014^{th} term of the series. 3, 5, 7…

**Solution:**

Based on our formula we need to know the first term and the common difference.

Given:

**Worked Problem 2:**

The nth term of an arithmetic series is given by the formula . Find the following;

(a). first term

(b). 2014^{th} term

(c). Common difference

**Solution:**

(a). first term:

Let n=1

(b)2014^{th} term

Let n=2014

(c). Common difference

In the common difference is the coefficient of n which is 3. If you want to check , try to solve for the second term and see for yourself. Technically, came from the general formula with known common difference d. Using distributive property we can rewrite the formula in . In the given expression , and making d=3.

**Worked Problem 3:**

The 4^{th} term of an arithmetic progression is 18 and the 10^{th} term is 42. Find the 100^{th} term.

**Solution:**

Now, we count how many terms from 4^{th} term to 10^{th} term.(4,5,6,7,8,9,10) making n=7.

From 4^{th} term to 100^{th} terms there are 100-3=97 terms. That is the 100 terms minus the first three terms.

### Dan

#### Latest posts by Dan (see all)

- 2016 MMC Schedule - November 4, 2015
- 2014 MTAP reviewer for Grade 3 - September 30, 2015
- 2015 MTAP reviewer for 4th year solution part 1 - August 22, 2015

Today, I went to the beach front with my children. I found a sea shell and gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She put the shell to her ear and screamed. There was a hermit crab inside and it pinched her ear. She never wants to go back! LoL I know this is totally off topic but I had to tell someone!

I’m also writing to let you know of the cool experience my daughter had checking yuor web blog. She learned several issues, including what it’s like to possess an amazing giving mindset to get most people without difficulty fully understand chosen tortuous issues. You really exceeded people’s expected results. Thank you for churning out such great, safe, educational and also unique tips on the topic.

I am curious to locate out what blog system you’re utilizing? Im having some small security problems with my latest site and Id like to find something a lot more risk-free. Do you’ve any suggestions? Hmm it looks like your weblog ate my initial comment (it was super long) so I guess Ill just sum it up what I wrote and say, Im thoroughly enjoying your weblog. I too am an aspiring weblog blogger but Im still new to everything. Do you’ve any guidelines and hints for rookie weblog writers? Id definitely appreciate it.

Your style is really unique compared to other folks

I have read stuff from. Thanks for posting when you’ve

got the opportunity, Guess I will just book mark this web site.

This is the perfect webpage for anyone who really

wants to find out about this topic. You know a whole lot its almost tough

to argue with you (not that I personally would want to…HaHa).

You certainly put a new spin on a subject that has been discussed for a

long time. Wonderful stuff, just excellent!

It’s going to be finish of mine day, but before end I am reading this impressive paragraph to increase my experience.

After looking at a few of the blog posts on your website, I seriously appreciate your way of writing a blog.

I bookmarked it to my bookmark webpage list and will be checking back soon. Take a

look at my web site as well and let me know your opinion. maglie calcio poco prezzo

I am curious to locate out what blog system you’re utilizing? Im having some small security problems with my latest site and Id like to find something a lot more risk-free. Do you’ve any suggestions? Hmm it looks like your weblog ate my initial comment (it was super long) so I guess Ill just sum it up what I wrote and say, Im thoroughly enjoying your weblog. I too am an aspiring weblog blogger but Im still new to everything. Do you’ve any guidelines and hints for rookie weblog writers? Id definitely appreciate it.

I would like to thank you for the efforts you have put in writing this blog.

I am hoping to see the same high-grade content from you in the future as

well. In truth, your creative writing abilities has encouraged me

to get my own, personal blog now 😉

After looking at a few of the blog posts on your website, I seriously appreciate your way of writing a blog.

Now, get a chance to study in abroad. Complete your MBBS in Georgia.