p : · If nth term of a sequence _is linear then sequence is in A.P.
Converse of statement p is

Options

A. If a sequence is not in A.P. then its nth term is linear
B. If a sequence is in A.P. then it's nth term is not linear
C. If a sequnce is in A.P. then its .11th term is linear
D. Both (1) & (2)

Answer

To find the converse of the statement \( p \), we follow these steps:

### Step 1: Understand the Original Statement
The original statement \( p \) is: "If the \( n \)th term of a sequence is linear, then the sequence is in A.P."
This can be expressed in the form of a conditional statement:
- Let \( P \): "The \( n \)th term of a sequence is linear."
- Let \( Q \): "The sequence is in A.P."

So, the statement can be written as \( P \implies Q \).

### Step 2: Identify the Converse
The converse of a statement \( P \implies Q \) is \( Q \implies P \). This means we need to switch the hypothesis and conclusion.

### Step 3: Write the Converse Statement
Based on the identification in Step 1, the converse of the original statement is:
"If the sequence is in A.P., then the \( n \)th term of the sequence is linear."

### Final Answer
Thus, the converse of the statement \( p \) is:
"If the sequence is in A.P., then the \( n \)th term of the sequence is linear."

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