Question

If 5th term of an A.P. is 11 and common difference is 2 then what is its first term ?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

To verify the answer, you can construct the A.P. with \(a=3\) and \(d=2\). The sequence is 3, 5, 7, 9, 11... The 5th term is indeed 11, which confirms the calculation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An Arithmetic Progression (A.P.) is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference (\(d\)). The nth term of an A.P. can be found using a standard formula.

Step 2: Key Formula or Approach:
The formula for the nth term (\(a_n\)) of an A.P. is:
\[ a_n = a + (n-1)d \] where \(a\) is the first term, \(n\) is the term number, and \(d\) is the common difference.

Step 3: Detailed Explanation:
We are given the following information:
The 5th term, \(a_5 = 11\).
The common difference, \(d = 2\).
The term number, \(n = 5\).
We need to find the first term, \(a\).
Substitute the given values into the formula:
\[ 11 = a + (5-1) \times 2 \] \[ 11 = a + (4) \times 2 \] \[ 11 = a + 8 \] To find \(a\), subtract 8 from both sides of the equation:
\[ a = 11 - 8 \] \[ a = 3 \] So, the first term of the A.P. is 3.

Step 4: Final Answer:
The first term of the A.P. is 3.