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# 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.

\(a_1,a_2,a_3,\ldots, a_{98} \) are terms in an arithmetic progression with common difference 1 such that their sum is 137.

What is the sum of the even terms of this progression? That is, what is the value of \( a_2+a_4+a_6+\cdots+a_{98} \)?

What is the largest positive integer that must be a divisor of the sum of an arithmetic sequence with 90 integer terms?

Try Part II

\[\large \frac ab \ , \ ab \ , \ a -b \ , \ a+b \]

Above shows real numbers that belong to an arithmetic progression in order. Find the next term of this sequence.

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