Find the next term of the A-P- -2-8-18-32-

The given A.P. is √(2), 2√(2), 3√(2), 4√(2), .....Common difference d = 2^nd term 1^st termd =2√(2) √(2)=√(2)Therefore, the next term is 4√(2)+d=4√(2)+√(2)=5√ ...

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Standard VI

Mathematics

Equivalent Fractions

Find the next...

Question

Find the next term of the A.P. $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, . . . . .$

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Solution

The given A.P. is $\sqrt{2}, 2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, . . . . .$
Common difference $d = 2^{n d}$ term $- 1^{s t}$ term
$d = 2 \sqrt{2} - \sqrt{2}$
$= \sqrt{2}$
Therefore, the next term is $4 \sqrt{2} + d$
$= 4 \sqrt{2} + \sqrt{2}$
$= 5 \sqrt{2}$ .
Hence, the next term is $5 \sqrt{2}$

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Find the next term of the A.P. √2,√8,√18,√32,.....

The given A.P. is √2,2√2,3√2,4√2,.....Common difference d=2nd term −1st termd=2√2−√2=√2Therefore, the next term is 4√2+d=4√2+√2=5√2.Hence, the next term is 5√2

Find the next term of the A.P. $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, . . . . .$

The given A.P. is $\sqrt{2}, 2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, . . . . .$
Common difference $d = 2^{n d}$ term $- 1^{s t}$ term
$d = 2 \sqrt{2} - \sqrt{2}$
$= \sqrt{2}$
Therefore, the next term is $4 \sqrt{2} + d$
$= 4 \sqrt{2} + \sqrt{2}$
$= 5 \sqrt{2}$ .
Hence, the next term is $5 \sqrt{2}$