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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. See more

# Finding the nth Term

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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