A) HP
B) GP
C) AP
D) none of these
Correct Answer: C
Solution :
Given series is \[\frac{5}{\sqrt{7}},\frac{6}{\sqrt{7}},\sqrt{7},...\] Now, \[{{d}_{1}}=\frac{6}{\sqrt{7}}-\frac{5}{\sqrt{7}},{{d}_{2}}=\sqrt{7}-\frac{6}{\sqrt{7}}\] i.e., \[{{d}_{1}}=\frac{1}{\sqrt{7}},{{d}_{2}}=\frac{7-6}{\sqrt{7}}=\frac{1}{\sqrt{7}}\] Here, \[{{d}_{1}}={{d}_{2}}\] Since, the common difference is same, therefore the given series is an AP. Note: (1) In an AP series, the common differences will be same. (2) In a GP series, the common ratios will be same.
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