Find the next term in the sequence six, 30, 150, 750, blank.
We’re told that this is a sequence, but we’re not given any specific information about what kind of sequence it is, which means we’ll need to first establish the pattern in this sequence before we can find that missing term. The pattern will be some rule that’s true for each of these terms. We’re asking, how do we get from six to 30? And then we need to apply that same operation to get from 30 to 150 and from 150 to 750.
Now, of course, six plus 24 does equal 30. But 30 plus 24 does not equal 150. So let’s try six times five, which equals 30. And five times 30 equals 150. And 150 times five equals 750. What’s happening here is we’re multiplying the previous term by five to get the next term in the sequence. And this fits the geometric sequence, making this sequence a geometric sequence with a common ratio of five. The next term in this sequence will be 750 times five, which is 3,750.