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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions2 Marks
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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