Show thet the followiong sequences is an A.P. Also, find the comm… - Vidyadip

Question

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$\sqrt{2},\ 3\sqrt{2},\ 5\sqrt{2},\ 7\sqrt{2},...$

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Answer

$\sqrt{2},3\sqrt{2},5\sqrt{2},7\sqrt{2},...$
$\text{a}_1=\sqrt{2},\text{a}_2=3\sqrt{2},\text{a}_3=5\sqrt{2},\text{a}_4=7\sqrt{2}$
$\text{a}_4-\text{a}_3=\text{a}_3-\text{a}_2=\text{a}_2-\text{a}_1=2\sqrt{2}$
$\therefore$ The comman dufference is $2\sqrt{2}$
and the given sequence is A.P
$\text{a}_5-\sqrt{2}+2\sqrt{2}(5-1)=9\sqrt{2}$
$\text{a}_6-\sqrt{2}+2\sqrt{2}(6-1)=11\sqrt{2}$
$\text{a}_7-\sqrt{2}+2\sqrt{2}(7-1)=13\sqrt{2}$

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