Waste less time on Facebook — follow Brilliant.
×

Arithmetic Progressions

What's the sum of the first 100 positive integers? How about the first 1000? Learn the fun and fast way to solve problems like this. See more

Level 1

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

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

What was Gauss' answer?

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


Image Source: Wikipedia.

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

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

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


Image Credit: Ricardo Liberato, CC SA 2.0

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.

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

×

Problem Loading...

Note Loading...

Set Loading...