A) \[\frac{2}{{{a}_{m+k}}+{{a}_{m-k}}}\]
B) \[\frac{{{a}_{m+k}}-{{a}_{m-k}}}{2}\]
C) \[\frac{{{a}_{m+k}}+{{a}_{m-k}}}{2}\]
D) None of these
Correct Answer: C
Solution :
\[{{a}_{m+k}}=A+(m+k-1)\,D\] and \[{{a}_{m-k}}=A+(m-k-1)\,D\] Adding both equations, we get \[\frac{{{a}_{m+k}}+{{a}_{m-k}}}{2}=A+(m-1)\,D={{a}_{m}}\].
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