Arithmetic sequence

Arithmetic sequences are similar to function, in that they indicate a way to work with numbers. However, instead of working with numbers continuously (including terms with decimals), sequences work only with whole numbers.

Questions will normally provide a sequence, which students will then have to determine a specific term in (for example, the 27th term in the sequence). However, students can also be given numbers from the sequence and asked to identify a formula that could be the sequence those numbers follow.

Here is an example question from the 2017 April ACT:

Here the question is looking for the 50th term in the sequence. The 3rd and 4ths terms of the sequence are given. Since there is no other information, the sequence likely has to be something quite simple.

There is an increase of 5 in between the 3rd and 4th terms, so the sequence might be: n_x = 5 + n_x − 1, where x_n is the current number of the sequence and x_n − 1is the previous number in the sequence.

Since the sequence increases by 5 every term, and there it will take 46 more terms to get from the 4th term to the 50th, that means the 50th term will be 46 x 5 = 230 greater than the 4th term.

Therefore the 50th term is 4th term + 230 = 18 + 230 = 248. So the answer is A.