To find the 18th term of the sequence 5, 8, 11, 14, 17, we first need to identify the pattern in the sequence. This is an arithmetic sequence since the difference between consecutive terms is constant.
Let’s start by looking at the terms:
- 1st term: 5
- 2nd term: 8
- 3rd term: 11
- 4th term: 14
- 5th term: 17
Next, we compute the common difference:
- 8 – 5 = 3
- 11 – 8 = 3
- 14 – 11 = 3
- 17 – 14 = 3
Thus, the common difference (d) is 3.
In an arithmetic sequence, the nth term can be found using the formula:
An = A1 + (n – 1) * d
Where:
- An is the nth term
- A1 is the first term (which is 5)
- d is the common difference (which is 3)
- n is the term number we want to find (which is 18)
Now, substituting the values into the formula:
A18 = 5 + (18 – 1) * 3
A18 = 5 + (17) * 3
A18 = 5 + 51
A18 = 56
Therefore, the 18th term of the sequence is 56.