Sum of First 10 Terms of an Arithmetic Progression (AP)
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. The general form of an arithmetic progression is given by \( a_n = a_1 + (n-1)d \), where \( a_n \) is the nth term, \( a_1 \) is the first term, n is the number of terms, and d is the common difference.

Given AP Term
In this case, the nth term of the AP is given by \( 2n + 1 \). To find the sum of the first 10 terms of this AP, we need to determine the first term and the common difference.

Find First Term and Common Difference
Since the nth term is \( 2n + 1 \), we can equate it to the general form of the nth term of an AP:
\( 2n + 1 = a_1 + (n-1)d \)
Comparing coefficients, we get:
\( a_1 = 1 \) (since the coefficient of n in the general form is 1)
\( d = 2 \) (since the coefficient of n in the given nth term is 2)

Calculate Sum of First 10 Terms
The sum of the first n terms of an AP is given by the formula: \( S_n = \frac{n}{2} [2a_1 + (n-1)d] \)
Substitute the values of \( a_1 = 1 \), \( d = 2 \), and \( n = 10 \) into the formula:
\( S_{10} = \frac{10}{2} [2(1) + (10-1)(2)] \)
\( S_{10} = 5[2 + 9(2)] \)
\( S_{10} = 5[2 + 18] \)
\( S_{10} = 5(20) \)
\( S_{10} = 100 \)
Therefore, the sum of the first 10 terms of the given AP is 100.