Question 2 (iii)
Verify that each of the following is an AP and then write its next three terms.
$\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}, \dots$

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Solution

$H e r e, a_{1} = \sqrt{3}, a_{2} = 2 \sqrt{3} a n d a_{3} = 3 \sqrt{3}$
$a_{2} - a_{1} = 2 \sqrt{3} - \sqrt{3} = \sqrt{3}, a_{3} - a_{2} = 3 \sqrt{3} - 2 \sqrt{3} = \sqrt{3}$
$∵ a_{2} - a_{1} = a_{3} - a_{2} = \sqrt{3} = C o m m o n d i f f e r e n c e$
Since the difference between successive terms are same, it forms an AP.
The next three terms are,
$a_{4} = a_{1} + 3 d = \sqrt{3} + 3 (\sqrt{3}) = 4 \sqrt{3}$
$a_{5} = a_{1} + 4 d = \sqrt{3} + 4 \sqrt{3} = 5 \sqrt{3}$
$a_{6} = a_{1} + 5 d = \sqrt{3} + 5 \sqrt{3} = 6 \sqrt{3}$

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