Question
Show that the progressions given below is an AP. Find the first term, common difference and next term.
$\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},\ ....$
$\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},\ ....$
✓
Answer
A sequence in which each term differs from its preceding term by a constant is called an AP.
$\sqrt{8}-\sqrt{2}=2\sqrt{2}-\sqrt{2}=\sqrt{2}$
$\sqrt{18}-(\sqrt{8})=3\sqrt{2}-(2\sqrt{2})=\sqrt{2}$
$\sqrt{32}-(\sqrt{18})=4\sqrt{2}-3\sqrt{2}=\sqrt{2}$
Clearly, the progression an AP.
The first term $=\sqrt{2}$
Common difference $=\sqrt{2}$
The next term $\sqrt{32}+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}=\sqrt{50}$
$\sqrt{8}-\sqrt{2}=2\sqrt{2}-\sqrt{2}=\sqrt{2}$
$\sqrt{18}-(\sqrt{8})=3\sqrt{2}-(2\sqrt{2})=\sqrt{2}$
$\sqrt{32}-(\sqrt{18})=4\sqrt{2}-3\sqrt{2}=\sqrt{2}$
Clearly, the progression an AP.
The first term $=\sqrt{2}$
Common difference $=\sqrt{2}$
The next term $\sqrt{32}+\sqrt{2}=4\sqrt{2}+\sqrt{2}=5\sqrt{2}=\sqrt{50}$
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