Question

25th term of an A.P. 6, 10, 14, ... will be:

• A. 100
• B. 102
• C. 101
• D. 151

Hint:

Always use $a_n = a + (n-1)d$ for finding terms in an A.P. Double-check the common difference $d$ before substituting.

Answer 1

The Correct Option is B

Step 1: Recall formula of the $n$th term of an A.P.
The $n$th term of an arithmetic progression is given by: \[ a_n = a + (n-1)d \] where $a =$ first term, $d =$ common difference.

Step 2: Identify values
First term $a = 6$
Common difference $d = 10 - 6 = 4$
We need the $25$th term $\,(n=25)$.

Step 3: Substitute values
\[ a_{25} = 6 + (25-1)\times 4 \] \[ = 6 + 24 \times 4 \] \[ = 6 + 96 \] \[ = 102 \]

Step 4: Conclusion
The $25$th term of the A.P. is $102$.
The correct answer is option (B).