Algebra

Arithmetic Progressions

Finding the nth Term - Arithmetic Progressions

         

If the 44 numbers

14,a,28,b14,\quad a,\quad 28,\quad b

form an arithmetic progression in that order, what is the sum of a a and b? 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 a1=2a_{1} = 2 and common difference d=6d = 6. What is the 5th term of the progression, a5a_{5}?

A frog is on the bottom of an empty well 108 m108\text{ m} deep. It climbs up the well 3 m3\text{ m} during the daytime and slips down 1 m1\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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