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Video: Finding the Following Term in a Given Sequence

Tim Burnham

Find the next term in the sequence 28, 37, 46, 55, 64, _.


Video Transcript

Find the next term in the sequence: twenty-eight thirty-seven forty-six fifty-five sixty-four. So we’ve been given five terms in a sequence. The first term is twenty-eight, the second term is thirty-seven, the third term forty-six, the fourth term is fifty-five, and the fifth term is sixty-four.

Now the fact that it’s been called a sequence tells us that there must be some sort of pattern that takes you from one number to the next number, some sort of common pattern that’s going on.

Well if I look at the first term and the second term, twenty-eight and thirty-seven, if I add nine to twenty-eight, I get thirty-seven. And also if I add nine to thirty-seven, I get forty-six. If I add nine to forty-six, I get fifty-five. And if I add nine to fifty-five, I get sixty-four.

So my pattern is that, to get from one term to the next term, I add nine. So to find the next term in my sequence, the sixth term, I need to add nine to sixty-four.

And that will give me seventy-three. So the answer is seventy-three. Now just a little bit of terminology before we go, in this kind of sequence where you add a constant number to each term to get the next term is called an arithmetic sequence.