Find Formula & Set Builder Notation for 2, 5, 9, 14, 20

Let’s analyze the differences between consecutive terms to find the pattern:

Notice that the differences are consecutive integers: 3, 4, 5, 6… This suggests that the formula involves adding consecutive numbers to the previous term.

Let’s break down each term:

We can see a pattern emerging: each term is the sum of consecutive integers up to a certain point.

We can express this pattern with a formula. Notice that:

This suggests the general formula:

where represents the nth term in the sequence.

Now, let’s express this set using set-builder notation:

This reads as “the set of all such that equals 1 plus n times (n plus 1) divided by 2, where n is an element of the set {1, 2, 3, 4, 5}.”