Arithmetic Progression: Calculating the 10th Term

The problem asks for the 10^th term of a given Arithmetic Progression (AP).

Understanding the Arithmetic Progression

• The sequence provided is 2, 7, 12, ...
• The first term ($a$) is 2.
• The common difference ($d$) is found by subtracting any term from its subsequent term: $7 - 2 = 5$ or $12 - 7 = 5$. Thus, $d = 5$.
• We need to find the 10^th term, so $n = 10$.

Step-by-Step Solution

The formula for the $n^{\text{th}}$ term of an Arithmetic Progression is:

$a_n = a + (n-1)d$

Substitute the known values into the formula:

• $a = 2$
• $d = 5$
• $n = 10$

Calculate the 10^th term ($a_{10}$):

$a_{10} = 2 + (10-1) \times 5$

$a_{10} = 2 + (9) \times 5$

$a_{10} = 2 + 45$

$a_{10} = 47$

The 10^th term of the Arithmetic Progression is 47.