Question

If P + 1, 2P + 1, 4P - 1 are in A.P. then the value of P is

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

To verify your answer, substitute P=2 back into the terms: (2+1), 2(2)+1, 4(2)-1 -> 3, 5, 7. The sequence is 3, 5, 7, which is an A.P. with a common difference of 2. This confirms the answer is correct.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
If three terms \(a, b, c\) are in an Arithmetic Progression (A.P.), then the difference between consecutive terms is constant. This means \(b - a = c - b\), which can be rearranged to \(2b = a + c\). The middle term is the arithmetic mean of the first and third terms.

Step 2: Key Formula or Approach:
We will use the property \(2 \times (\text{middle term}) = (\text{first term}) + (\text{third term})\).

Step 3: Detailed Explanation:
The given terms are:
First term: \(a = P + 1\)
Middle term: \(b = 2P + 1\)
Third term: \(c = 4P - 1\)
Apply the A.P. property:
\[ 2(2P + 1) = (P + 1) + (4P - 1) \] Expand both sides:
\[ 4P + 2 = P + 4P + 1 - 1 \] \[ 4P + 2 = 5P \] Now, solve for P:
\[ 2 = 5P - 4P \] \[ P = 2 \]

Step 4: Final Answer:
The value of P is 2.