Question

The missing term in the series 1, 4, 27, 16, ?, 36, 243, explain

Answer 1

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♦ Sequence and series ♦

► Above sequence can be observed as : 1³ , 2², 3³, 4², ...

 → A logical approach might say : " The odd numbers are raised by power 3         while  an even number is raised by a 2 "
 → The missing term is : 5³ = 125

 • However, a friend once asked if Generalizations can happen for Logical Series, so, the following generalization might help as well :-
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 • The generalization takes place as :
      $t_n = (n)^{2.5 -(-1)^n(0.5)}$

 • Hence, following the generalized term : t(5) = 5³ = 125

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→ Hope it helped