Question

Find the next no in sequence 1,3,9,21,41,71,?

Answer 1

Answer:

Our first task for solving this problem is to crack the series. If you will gave a closer look on the series, for a general n-th term the value will be (Σn2)+(Σn)+1, where

(Σn2): is sum of squares of first n-natural numbers.

(Σn): is sum of first n-natural numbers.

1 is a simple constant value.

So, for calculating any n-th term of given series say f(n) we have:

f(n) = (Σn2)+(Σn)+1

= ( ((n*(n+1)*(2n+1))/6) + (n*(n+1)/2) + 1

= (n3+ 3n2 + 2n + 3 ) /3

Answer 2

Solution :-

Logic :- Previous term + n² + n = Next term .

Explanation :-

→ 1 + 1² + 1 = 1 + 1 + 1 = 3

→ 3 + 2² + 2 = 3 + 4 + 2 = 9

→ 9 + 3² + 3 = 9 + 9 + 3 = 21

→ 21 + 4² + 4 = 21 + 16 + 4 = 41

→ 41 + 5² + 5 = 41 + 25 + 5 = 71

→ 71 + 6² + 6 = 71 + 36 + 6 = 113 (Ans.)

Hence, the next number in sequence will be 113 .

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