Question

what should come in place of question mark. 11,36,?,178,364.​

Answer 1

The missing number in the given pattern is "84" according to the following logic of doubling and adding.

The logic of the given pattern is :

The following number is twice the previous plus some value "d". The value "d" is initially 14 and decreases by 2 in each iteration step.

Thus, From $x_{1}$ to $x_{2}$ :  

Initial d = 14

$x_{2} = (2*x_{1} ) + d \\x_{2} = (2*11 ) + 14 \\x_{2} = 22+14\\ x_{2} = 36$

From $x_{2}$ to $x_{3}$ :  

New difference "d" = 14 - 2 = 12

$x_{3} = (2*x_{2} ) + d \\x_{3} = (2*36 ) + 12 \\x_{3} = 72+12\\ x_{3} = 84$

From $x_{3}$ to $x_{4}$ :  

New difference "d" = 12 - 2 = 10

$x_{4} = (2*x_{3} ) + d \\x_{4} = (2*84 ) + 10 \\x_{4} = 168+10\\ x_{4} = 178$

From $x_{4}$ to $x_{5}$ :  

New difference "d"= 10 - 2 = 8

$x_{5} = (2*x_{4} ) + d \\x_{5} = (2*178 ) + 8 \\x_{5} = 356+8\\ x_{5} = 364$

Thus, the logic is that the Nth term is twice the (N-1)th term with a common difference "d" added to it. The difference "d" is initialized by 14 and decreases by 2 units every time.

Hence, the missing term in the pattern is "84".

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Answer 2

the missing number in the sequence is 88

To determine the missing number in the sequence 11, 36, ?, 178, 364, we need to identify the pattern or rule that governs the sequence. One possible rule is that each term in the sequence is obtained by multiplying the previous term by a constant factor and then adding a specific value.

If we apply this rule to the sequence, we get:

The second term (36) is obtained by multiplying the first term (11) by 3 and then adding 3: 11 x 3 + 3 = 36

The third term (? ) is obtained by multiplying the second term (36) by 5 and then subtracting 2: 36 x 5 - 2 = 178

The fourth term (178) is obtained by multiplying the third term (?) by 2 and then adding 2: ? x 2 + 2 = 178

The fifth term (364) is obtained by multiplying the fourth term (178) by 2 and then subtracting 2: 178 x 2 - 2 = 364

Using the equation for the fourth term, we can solve for the missing number:

? x 2 + 2 = 178

? x 2 = 178 - 2

? x 2 = 176

? = 88

Therefore, the missing number in the sequence is 88.

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