What is the nth-term of this sequence? 29, 26, 23, 20, 17...

First you need to find the difference between the terms. (The difference is how we get from one term to another.) In this case the difference is -3 because 26 - 29 = -3, 23 - 26 = -3 and so on. For a linear sequence (which this is) all the differences should be the same. The difference in the number that goes in front of the n. So our nth term currently looks like this: -3n. However, if we look at the sequence with nth term 6n we get this sequence: -3, -6, -9, -12... which is not the sequence we have so we need to adapt our nth term to match our sequence. The difference between the first term our our sequence and the first term of the -3n sequence is 29 - (-3) = 32. The means we need to add 32 to -3n to get the nth term. Our nth term is -3n+32. We can check this by checking the 2nd term: -3(2)+32 = 26 which matches so we know its right.