[tex]The\ given\ number\ of\ series\ is: \\ \\ \{ 10,\ 12,\ 22,\ 34,\ 56,\ 90 \} \\ \\ The\ problem\ that\ needed\ to\ be\ solved\ is: \\ \\ \{ 10,\ 12,\ 22,\ 34,\ 56,\ 90 ,\ ?\} \\ \\ \bold{Solution:} \\ \\ \bold{Hint:} \\ If\ you\ are\ ask\ to\ get\ the\ next\ term/number, \\ used\ trial\ and\ error\ always. \\ \\ To\ solve\ this\ kind\ of\ series, \\ \underline{get\ the\ difference\ between\ the\ number\ to } \\ \underline{the\ other\ number\ \underline{consecutively}} [/tex]
[tex].\ \ \ \ \ \ \ \ \ \boxed{^{\bold{\underline{Difference}}}} \\ . \ \ \ \ \ \ \ \ \ \ \ \ \downarrow \\ 10-12\to2 \\ 12-22\to10 \\ 22-34\to12 \\ 34-56\to22 \\ 56-90\to34 \\ \\ ^{If\ you\ want\ to\ ask\ me\ what\ is\ the\ purpose\ of\ getting\ the\ difference...} \\ ^{\bold{Then\ here's\ the\ answer...}} \\ \\ Add\ the\ following\ difference\ to\ get\ the\ \underline{\bold{\underline{difference}}\ of\ \bold{?\ and\ 90}}: \\ \\ 2+10\to12 \\ 10+12\to22 \\ 12+22\to34 \\ 22+34\to\boxed{56} [/tex]
[tex]Therefore,\ \bold{56\ is\ the\ awaited\ difference}\ to\ get\ the\ final\ answer. \\ \\ \bold{Add}\ the\ last\ set\ of\ number\ which\ is\ \bold{90\ to\ 56}\ to\ get\ \\ the\ value\ of\ the\ next\ number. \\ \\ \boxed{90+56=\underline{\bold{146}}} \\ \\ Therefore,\ the\ value\ of\ the\ next\ number\ is\ \bold{146}. \\ \\ The\ complete\ set\ of\ the\ number\ series\ is: \\ \\ \{10,\ 12,\ 22,\ 34,\ 56,\ 90,\ \bold{146}\} \\ \\ \\ Hope\ it\ Helps :) \\ Domini[/tex]
