Question

2, 4, 7, 12, 21, complete the series.

options:

1. 38
2. 36
3. 35
4. 33​

Answer 1

(.1) 38 is the answer thanks

Answer 2

Option 1 : The missing number in the given pattern is "38" according to the following logic of doubling and subtracting a serial number.

The logic of the series is : The following number is obtained by doubling the previous number and subtracting a number "d" from it. The value of d is initialized with 0 and increases by 1 in every iteration.

From  $x_{1}$ to $x_{2}$ :

Initial d = 0

$x_{2} = (2*x_{1} )-d\\x_{2} = (2*2 )-0\\ x_{2} = 4$

From  $x_{2}$ to $x_{3}$ :

New difference "d" = 0+1 = 1

$x_{3} = (2*x_{2} )-d\\x_{3} = (2*4 )-1\\ x_{3} = 8-1\\ x_{3} = 7$

Hence, In general for the Nth term, the difference "d" subtracted is (N-2)

               $x_{n} = (2*x_{n-1}) - (n-2) \\x_{n} = (2*x_{n-1}) - n+2$

Thus, for finding the 6th term, n = 6 :

               $x_{n} = (2*x_{n-1}) - (n-2) \\x_{6} = (2*x_{6-1}) - (6-2) \\x_{6} = (2*x_{5}) - (4) \\ x_{6} = (2*21) - (6-2)\\ x_{6} = 42 - 4\\ x_{6} = 38$

Thus, the logic is that the Nth term is twice the (N-1)th term with a common difference "d" subtracted from it. The difference "d" is initialized by 0 and increases by 1 unit every time.

Hence, the missing term in the pattern is "38".

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