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a) as we see over here A1=1^2
![a2 = {2}^{2} \\ \\ \\ similarly \: we \: get \: that \: \\ \\ a10 \: = {10}^{2} \\ \\ = 100 a2 = {2}^{2} \\ \\ \\ similarly \: we \: get \: that \: \\ \\ a10 \: = {10}^{2} \\ \\ = 100](https://tex.z-dn.net/?f=a2+%3D++%7B2%7D%5E%7B2%7D++%5C%5C++%5C%5C++%5C%5C+similarly+%5C%3A+we+%5C%3A+get+%5C%3A+that+%5C%3A++%5C%5C++%5C%5C+a10+%5C%3A++%3D++%7B10%7D%5E%7B2%7D++%5C%5C++%5C%5C++%3D+100)
![b ) = we \: get \: different \: remainders \: on \: diving \: perfect \: squares \: by \: 3 b ) = we \: get \: different \: remainders \: on \: diving \: perfect \: squares \: by \: 3](https://tex.z-dn.net/?f=b+%29+%3D++we+%5C%3A+get+%5C%3A+different+%5C%3A+remainders+%5C%3A+on+%5C%3A+diving+%5C%3A+perfect+%5C%3A+squares+%5C%3A+by+%5C%3A+3)
![c) \: = {3}^{2} . {6}^{2} . {9}^{2} .... \\ squareof \: all \: those \: which \: are \: multiple \: of \: 3 c) \: = {3}^{2} . {6}^{2} . {9}^{2} .... \\ squareof \: all \: those \: which \: are \: multiple \: of \: 3](https://tex.z-dn.net/?f=c%29+%5C%3A++%3D++%7B3%7D%5E%7B2%7D+.+%7B6%7D%5E%7B2%7D+.+%7B9%7D%5E%7B2%7D+....+%5C%5C+squareof+%5C%3A+all+%5C%3A+those+%5C%3A+which+%5C%3A+are+%5C%3A+multiple+%5C%3A+of+%5C%3A+3)
![d) \: = as \: we \: saw \: in \: the \: above \: sequence \: nth \: term \: = {n}^{2} \\ \\ \\ thus \: 10nth \: term \: will \: be \: (3 \times 10) \: whole \: square \: \\ \\ = 900 d) \: = as \: we \: saw \: in \: the \: above \: sequence \: nth \: term \: = {n}^{2} \\ \\ \\ thus \: 10nth \: term \: will \: be \: (3 \times 10) \: whole \: square \: \\ \\ = 900](https://tex.z-dn.net/?f=d%29+%5C%3A++%3D+as+%5C%3A+we+%5C%3A+saw+%5C%3A+in+%5C%3A+the+%5C%3A+above+%5C%3A+sequence+%5C%3A++nth+%5C%3A+term+%5C%3A++%3D++%7Bn%7D%5E%7B2%7D+++%5C%5C++%5C%5C++%5C%5C+thus+%5C%3A+10nth+%5C%3A+term+%5C%3A+will+%5C%3A+be+%5C%3A+%283+%5Ctimes+10%29+%5C%3A+whole+%5C%3A+square+%5C%3A++%5C%5C++%5C%5C++%3D+900)
![e) \: = the \: remainders \: will \: be \: \: 1 \: in \: all \: these \: cases. e) \: = the \: remainders \: will \: be \: \: 1 \: in \: all \: these \: cases.](https://tex.z-dn.net/?f=e%29+%5C%3A+++%3D+the+%5C%3A+remainders+%5C%3A+will+%5C%3A+be+%5C%3A++%5C%3A+1+%5C%3A+in+%5C%3A+all+%5C%3A+these+%5C%3A+cases.)
![f) \: = \: -24 \: . \: - 23 \: . \: ...... f) \: = \: -24 \: . \: - 23 \: . \: ......](https://tex.z-dn.net/?f=f%29+%5C%3A++%3D++%5C%3A++-24+%5C%3A+.+%5C%3A++-+23+%5C%3A+.+%5C%3A+......)
![|hope \: this\: might \: help \: you \: | |hope \: this\: might \: help \: you \: |](https://tex.z-dn.net/?f=+%7Chope+%5C%3A+this%5C%3A+might+%5C%3A+help+%5C%3A+you+%5C%3A+%7C+)
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