To find the 59th term of an arithmetic progression (AP), we can use the formula for the nth term of an AP:

$a_n = a_1 + (n - 1) \cdot d$

Where:

• $a_n$ is the nth term,
• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Given:

• $a_1 = 45$,
• $d = 7$,
• $n = 59$,

Substitute the values into the formula:

$a_{59} = 45 + (59 - 1) \cdot 7$ $a_{59} = 45 + 58 \cdot 7$ $a_{59} = 45 + 406$ $a_{59} = 451$

Thus, the 59th term of the arithmetic progression is $451$.

Would you like more details on this, or do you have any questions?

Here are some related questions to consider:

1. How do you find the sum of the first $n$ terms of an arithmetic progression?
2. What is the formula for the sum of an arithmetic series?
3. How do you determine if a sequence is arithmetic?
4. What happens when the common difference of an arithmetic progression is negative?
5. How does an arithmetic progression differ from a geometric progression?

Tip: In arithmetic sequences, the common difference ($d$) remains constant, so the pattern grows or decreases linearly!