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1 mark

In the following question, select the missing number from the given series.
56, 65, 81, 106, ?, 191

  1. A
    142
  2. B
    164
  3. C
    138
  4. D
    154

Solution & Step-by-step Explanation

Let's find the differences between the consecutive numbers:
65−56=9=3
2


81−65=16=4
2


106−81=25=5
2


The pattern shows that the differences are squares of consecutive natural numbers starting from 3:

3
2
,4
2
,5
2
,6
2
,7
2
,…
Following the pattern, the next difference must be 6
2
=36:

Missing number=106+36=142
Let's cross-check for the next term:

142+7
2
=142+49=191
This is perfectly consistent.

Practice this question

Try it yourself before checking the explanation above.

In the following question, select the missing number from the given series.
56, 65, 81, 106, ?, 191
A
142
B
164
C
138
D
154

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