Q. Consider the following statement : 1. If $a_{n}$ denotes the $n$th term of an AP, then $a_{n} = \frac{a_{n + k} + a_{n - k}}{2}$ 2. In an AP, if the sum of $m$ term is equal to the sum of $n$ terms, then the sum of $(m + n)$ term is always zero. 3. The sum to infinity of the series $\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + ...is\frac{1}{2}$. Which of the statement is given above is/are correct?
A) (1)and (2)
B) (2)and (3)
C) (3)and (1)
D) All (1), (2) and (3)
Explanation
The correct answer is Option D: All (1), (2) and (3).
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.