Which of the following form an AP? Justify your answer. (i) √3, √12, √27, √48, …

Home » Which of the following form an AP? Justify your answer. (i) √3, √12, √27, √48, …

Which of the following form an AP? Justify your answer.
(i) √3, √12, √27, √48, …

Which of the following form an AP? Justify your answer.
(i) √3, √12, √27, √48, …

Solution:

We have,

${{a}_{1~}}=\text{ }\surd 3$ $,{{a}_{2}}~=\text{ }\surd 12,\text{ }{{a}_{3}}~=\text{ }\surd 27$ and ${{a}_{4}}~=\text{ }\surd 48$

${{a}_{2}}~-{{a}_{1~}}=\text{ }\surd 12-\surd 3\text{ }=\text{ }2\surd 3-\surd 3\text{ }=\text{ }\surd 3$

${{a}_{3}}~-{{a}_{2~}}=\text{ }\surd 27-\surd 12\text{ }=\text{ }3\surd 3-2\surd 3\text{ }=\text{ }\surd 3$

${{a}_{4}}~-{{a}_{3~}}=\text{ }\surd 48-\surd 27\text{ }=\text{ }4\surd 3-3\surd 3\text{ }=\text{ }\surd 3$

We can clearly say that, the difference of successive terms is same, hence the given list of numbers from an AP.

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