Since a 1 = 1 and r = 2, we can substitute to get… Let's first find our explicit rule for this thing and then use it to get our terms. List the first four terms and the 20th term of a geometric sequence with a first term of 1 and a common ratio of 2. Just multiply the previous term by the common ratio. It'll be worth it.Īnd yeah, geometric sequences can also be written using a recursive rule. You're probably going to want to commit that general form equation thingy to memory. This means that the n th term, a n, is just the first term multiplied by the common ratio, r, to the ( n – 1) th power. The other thing it might be helpful to know at this point is the general form of a geometric sequence's explicit rule. In this sequence, each number is half the previous number, so it's fairly easy to see that we're multiplying by ½.
This is a completely normal thing for geometric sequences, by the way. Instead of multiplying by a whole number, we're going to have to multiply by a fraction. Remember, the common ratio is just the number we multiply by to get to the next term in a geometric sequence. The common ratio in that geometric sequence is r =. The constant that we're multiplying each term by (2 in this case) is called the common ratio, which we usually represent with the letter r. What else is new? All you need to remember is that while arithmetic sequences add some number to get the next term, geometric sequences multiply each term by some number. It's our experience that people tend to wig out by the time they get to geometric sequences.