# Question Video: Finding the Next Term in an Arithmetic Sequence

Find the next term in this sequence. 51, 102, 153, _.

01:35

### Video Transcript

Find the next term in this sequence. 51, 102, 153. What’s next?

The first question we should ask is what is being added to each term. Last time, that was really easy because it was two. If you don’t immediately recognise what’s being added, here’s what you can do. You can take the term in the second position and subtract the term in the first position. 102 minus 51 is 51. You could also subtract 102 from 53 or the position two number from the position three number. Both of these equal 51. 51 is what is being added each time.

To find the next term, we need to take the third term, 153, and add 51 to that. The next term in this sequence is 204. Here’s what a table for this sequence would look like. The operation here would be to take the position and multiply it by 51 because 51 is what we’re adding here. 51𝑛 would be the expression that we could use to take any position and find its value.