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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.

Finding the nth Term - Arithmetic Progressions


If the \(4\) numbers \[14, a, 28 , b\] form an arithmetic progression, what is sum of \( a \) and \( b?\)

You love marbles and start collecting them. You have 2 marbles initially and add the same number of marbles to your store each day. If you have 17 marbles total after 5 days, then how many marbles did you add each day?

An arithmetic progression has first term \(a_{1} = 2\) and common difference \(d = 6\). What is the 5th term of the progression, \(a_{5}\)?

A frog is on the bottom of an empty well \(108\text{ m}\) deep. It climbs up the well \(3\text{ m}\) during the daytime and slips down \(1\text{ m}\) at nighttime. What is the number of days it takes for the frog to be out of the well?

Suppose that when you are a teenager, your height increases at a steady rate of 3 inches every year. If your present height is 48 inches, then how many years will you take to grow to 66 inches tall?


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