The nth term of a progression is 2n+3. Show that it is an A.P. Also find is 10th term.

Explanation

To determine whether the given progression is an Arithmetic Progression (A.P.) and to find its 10th term, we can follow these steps:

### Step 1: Identify the nth term
The nth term of the progression is given as:
\[ a_n = 2n + 3 \]

### Step 2: Find the (n-1)th term
To find the (n-1)th term, we substitute \( n-1 \) into the formula:
\[ a_{n-1} = 2(n-1) + 3 \]
\[ a_{n-1} = 2n - 2 + 3 \]
\[ a_{n-1} = 2n + 1 \]

### Step 3: Calculate the common difference
The common difference \( d \) of an A.P. is defined as:
\[ d = a_n - a_{n-1} \]
Substituting the values we found:
\[ d = (2n + 3) - (2n + 1) \]
\[ d = 2n + 3 - 2n - 1 \]
\[ d = 2 \]

Since the common difference \( d \) is a constant (2), we can conclude that the sequence is indeed an A.P.

### Step 4: Find the 10th term
To find the 10th term, we substitute \( n = 10 \) into the nth term formula:
\[ a_{10} = 2(10) + 3 \]
\[ a_{10} = 20 + 3 \]
\[ a_{10} = 23 \]

### Conclusion
The sequence defined by the nth term \( 2n + 3 \) is an Arithmetic Progression, and the 10th term of this progression is:
\[ \boxed{23} \]

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