What is the general term of the sequence 3, 8, 13, 18, ...?

The general term of a sequence is a formula that allows us to compute any term in the sequence given its position (n).

In this case, the sequence is 3, 8, 13, 18, ...

To find the general term, we need to look for a pattern in the given terms.

Looking closely, we can observe that each term in the sequence is obtained by adding 5 to the previous term.

The first term, 3, is followed by adding 5 to get the second term, 8. Then, adding 5 to 8 gives us the third term, 13. Continuing this pattern, adding 5 to 13 gives us the fourth term, 18.

Therefore, the general term of this sequence is 5n - 2.

This can be understood as follows:

Let's consider the position of a term, n. To find the value of that term in the sequence, we multiply the position number, n, by 5 and subtract 2 from it.

For example:

• For n = 1, the general term becomes 5(1) - 2 = 3, which is the first term in the sequence.
• For n = 2, the general term becomes 5(2) - 2 = 8, which is the second term in the sequence.
• For n = 3, the general term becomes 5(3) - 2 = 13, which is the third term in the sequence.
• For n = 4, the general term becomes 5(4) - 2 = 18, which is the fourth term in the sequence.

Hence, the answer is 5n - 2