Question

Find the term 5, 22, ?, 140, 265

Answer 1

Answer:

63

Step-by-step explanation:

Let x be the Number.

5               22              x                140                 265

   17                  x-22         140-x           125

         x-39                162-2x         x-15

                  162-3x+39         3x-15-162

Now, for sequence to converge,

162 - 3x + 39 = 3x - 15 - 162

Therefore, 201 - 3x = 3x -177

Therefore, 6x = 378

Therefore, x = 63

So, missing number is 63. Series will converge at 4th level with it.

Answer 2

Answer:

The missing number is 63.

Step-by-step explanation:

Given sequence,

5, 22, ?, 140, 265,

By examining the sequence it is hard to find the missing number that follows the sequence,

Let n be the missing number,

The sequence would be,

5, 22, p, 140, 265

Since, In a logical sequence the final difference in the consecutive terms is always equal,

First difference = 22 - 5, p - 22, 140, - p, 265 - 140

Second difference = (p-22)-(22-5), (140-p)-(p-22), (265-140)-(140-p)

Third difference = [(140-p)-(p-22)]-[(p-22)-(22-5)], [(265-140)-(140-p)]-[(140-p)-(p-22)]

By the above statement,

[(140-p)-(p-22)]-[(p-22)-(22-5)] = [(265-140)-(140-p)]-[(140-p)-(p-22)]

140 - p - p + 22 - p + 22 + 22 - 5 = 265 - 140 - 140 + p - 140 + p + p - 22

201 - 3p = -177 + 3p

⇒ 6p = 378 ⇒ p =  63

Hence, missing number is 63.