examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Algebra
# Arithmetic Progressions

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

As a young boy, Gauss was able to calculate math quickly. He was asked for the value of

###### Image Source: Wikipedia.

\[ 1 +2 + 3 + \cdots + 100. \]

What was Gauss' answer?

**Hint**: \(1 + 2 + 3 + \cdots + n = \frac 12 n(n+1) \).

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Victor Paes Plinio**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

An arithmetic sequence has 11 terms which sum to 220. What is the middle (6th) term in the sequence?

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Mohamed Ahmed Abd El-F...**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

What is the value of \( n \) in the following expression?

###### Image Credit: Ricardo Liberato, CC SA 2.0

\[ 1 + 2 + 3 + \dots + (n-1) + n + (n-1) + \dots + 3 + 2 + 1 = 289 \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Arron Kau**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

In an arithmetic progression of 200 terms,

the 27th term equals to 2,

the 174th term equals to 4.

Find the sum of all the terms of the arithmetic progression.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Somesh Singh**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

\[\large 100+99+98+97+96+\cdots + 50 = \ ? \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Sign up to access problem solutions.

by
**
Dharma Teja**

Are you sure you want to view the solution?

Cancel
Yes I'm sure

×

Problem Loading...

Note Loading...

Set Loading...