Final answer:
The 59th term of the sequence 29, 37, 45 is 493. The sequence is arithmetic with a common difference of 8. Applying the formula for the nth term of an arithmetic sequence, we calculate the 59th term as 493.
Step-by-step explanation:
Finding the 59th Term of an Arithmetic Sequence
To find the 59th term of the sequence (29, 37, 45), we first need to determine the common difference of the sequence. We do this by subtracting any term from the term that follows it. For example:
37 - 29 = 8
45 - 37 = 8
The common difference is 8.
This sequence is an arithmetic sequence where each term increases by 8 from the previous term. The formula to find the nth term of an arithmetic sequence is:
an = a1 + (n - 1) * d
where:
- an is the nth term we want to find,
- a1 is the first term of the sequence,
- n is the term number,
- d is the common difference.
Plugging in the values for the 59th term:
a59 = 29 + (59 - 1) * 8
a59 = 29 + 58 * 8
a59 = 29 + 464
a59 = 493
Therefore, the 59th term of the sequence is 493.