Arithmetic Progressions
If the \(4\) numbers
\[14,\quad a,\quad 28,\quad b\]
form an arithmetic progression in that order, what is the 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?