Question

what is the next number in the series 7,23,31,55,109​

Answer 1

$Given \: series \: 7,23,31,55,109$

/* Observing the series , we can find following pattern */

$i) First \:term$

$= 2^{3} - \pink{1^{2}}$

$= 8-1$

$=7$

$ii) Second \:term$

$= 3^{3} - \pink{2^{2}}$

$= 27-4$

$=23$

$iii) Third \:term$

$= 4^{3} - \pink{3^{2}}$

$= 64 - 9$

$= 55$

$iv) Fourth \:term$

$= 5^{3} - \pink{4^{2}}$

$= 125 - 16$

$= 109$

$v) \red{next \:term }$

$= 6^{3} - \pink{5^{2}}$

$= 216 - 25$

$\green {= 191}$

Therefore.,

$\red{ Required \:next \: number }\green { = 191 }$

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