Sequences, especially arithmetic and geometric ones, are good for word problems.
Sequence story problems come in two main flavors. If these flavors were ice cream, they'd be vanilla and rocky road. We may have to find
In general, it's good strategy to write out the first few terms of the sequence in question so we can see the pattern of the terms. Maybe we can do it with ice cream cone in hand.
An old story goes that a peasant won a reward from the king, and asked for rice: one grain to be placed on the first square of a chessboard, two grains on the second square, four on the third square, and so on. Each square was to contain double the number of grains on the previous square.
If we look at the first few terms, we can see the pattern:
The nth square contains 2n – 1 grains of rice. We have
an = 2n – 1
where n is the square and an is how many grains of rice are on that square. Now we're prepared to answer the questions.
Be Careful: One type of sequence problem asks us to find a value of an. Another asks us to find a value of n. We should be sure to provide the correct information in our answer.
Sometimes when we're asked to find a value of n, we might solve an equation or inequality and get a value of n that isn't a whole number. This is where the road can get bumpy, so we could take a lick of our rocky road cone, and then we'd try out the whole numbers to either side and see which gives a better answer.