(b) These are the first five terms of a sequence. Find the \( n \)th term of the sequence.

To find the nth term of your sequence, a bit of investigation is key! Start by identifying the pattern from the given first five terms. If they increase in a consistent way, it could be arithmetic (by adding a certain number), or it might be geometric (by multiplying). Once you spot the pattern, you can express the nth term using a formula. For example, if your sequence's first term is \( a_1 \) and you find the common difference \( d \), the nth term can be written as \( a_n = a_1 + (n-1) \cdot d \). Now, let's avoid some common pitfalls! When analyzing the terms, it's easy to overlook non-linear patterns or assume a polynomial form too quickly. That means keeping an open mind about other kinds of relationships! Be sure to analyze differences or ratios properly if the pattern is not blatantly obvious. And remember, double-check your formula by plugging in some known values to ensure it's working as expected!