To find the \(12^{\text{th}}\) term of an Arithmetic Progression (A.P.) where the first few terms are given as 2, 6, 10, we will follow these steps:
1. Identify the first term (a) of the A.P.:
The first term \(a\) is 2.
2. Determine the common difference (d):
The common difference \(d\) can be found by subtracting any term from the subsequent term. For example:
[tex]\[
d = 6 - 2 = 4
\][/tex]
3. Use the formula for the \(n\)th term of an A.P.:
The formula to find the \(n\)th term of an A.P. is
[tex]\[
a_n = a + (n - 1) \cdot d
\][/tex]
Here, we need to find the \(12^{\text{th}}\) term, so \(n = 12\).
4. Substitute the values into the formula:
[tex]\[
a_{12} = 2 + (12 - 1) \cdot 4
\][/tex]
5. Simplify the equation:
[tex]\[
a_{12} = 2 + 11 \cdot 4
\][/tex]
[tex]\[
a_{12} = 2 + 44
\][/tex]
6. Calculate the result:
[tex]\[
a_{12} = 46
\][/tex]
Hence, the [tex]\(12^{\text{th}}\)[/tex] term of the A.P. is 46.
