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GATEEC_01 2014 5

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725

 

35-12=23

81-35=46=23*2

173-81=92=46*2

357-173=184=92*2

x-357=184*2

x=357+184*2=725
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$T_n = 2 \times T_{n-1} + 11.$

So, $T_6 = 2 \times T_5 + 11 \\= 2 \times 357 + 11 \\= 725.$
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81 = 35*3 - 12*2

173 = 81*3 - 35*2

357 = 173*3 - 81*2

Next number 

357*3 - 173*2 = 725

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