1.

5 ,6, 14 ,41, 105, ?​

Answer» EN :-
  • A Number series is given to us .
  • 5 , 6 , 14 , 41 , 105 .

To FinD :-

  • The next number .

SolutioN :-

The first thing that comes in our mind is to subtract the consecutive terms and see if their difference follow certain pattern or not . So let's subtract the consecutive terms .

\boxed{\begin{array}{c|c} \underline{\textsf{\textbf{ Consecutive terms }}}&\underline{\textsf{\textbf{ Their Difference }}}\\\\\sf 6 - 5 &\red{\sf <klux>1</klux> }\\ \\ \sf 14 - 6 &\red{\sf 8 } \\\\\sf 41 - 14 &\red{\sf <klux>27</klux> } \\\\\sf 105 - 41 & \red{\sf 64 } \end{array} }

The difference of the consecutive terms we got is , 1 ,8 , 27 , 64 . If we notice then we can see that these are the cube of first 4 natural numbers that is 1 , 2 , 3 & 4 . We can write , 1 as 1³ , 8 as 2³ and so on . Hence the next number to be added is of cube of 5 that is 5³ = 125 . Therefore on adding 125 to 105 , we have 230.

Hence the next term in this series is 230 .



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