Which of the following form an AP? Justify your answer. (i) 1, 1, 2, 2, 3, 3… (ii) 11, 22, 33…

Home » Which of the following form an AP? Justify your answer. (i) 1, 1, 2, 2, 3, 3… (ii) 11, 22, 33…

Which of the following form an AP? Justify your answer.
(i) 1, 1, 2, 2, 3, 3…
(ii) 11, 22, 33…

Which of the following form an AP? Justify your answer.
(i) 1, 1, 2, 2, 3, 3…
(ii) 11, 22, 33…

Solution:

(i) We have ${{a}_{1}}~=\text{ }1\text{ },\text{ }{{a}_{2}}~=\text{ }1,\text{ }{{a}_{3}}~=\text{ }2$ and ${{a}_{4}}~=\text{ }2$

${{a}_{2}}~-{{a}_{1}}~=\text{ }0$

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

We can clearly say that, the difference of successive terms is not same, hence the given list of numbers does not form an AP.

(ii) We have ${{a}_{1}}~=\text{ }11,\text{ }{{a}_{2}}~=\text{ }22$ and ${{a}_{3}}~=\text{ }33$

${{a}_{2}}~-{{a}_{1}}~=\text{ }11$

${{a}_{3}}~-{{a}_{2}}~=\text{ }11$

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

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