What is the 59th term of an arithmetic progression with initial term 45 and common difference 7

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!

What is the 59th term of an arithmetic progression with initial term 45 and common difference 7?

Find the 59th term of an arithmetic progression where the first term is 45 and the common difference is 7. Learn how to apply the arithmetic progression formula to solve sequence problems. Suitable for Grades 6-8 students.

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