Correct option is C
Given:
The sequence is: 6,25,62,123,214,3416, 25, 62, 123, 214, 3416,25,62,123,214,341.
We need to determine the next number by finding a simpler pattern.
Solution:
Calculate the differences between consecutive terms:
25−6=19,62−25=37,123−62=61,214−123=91,341−214=127.25 - 6 = 19, \quad 62 - 25 = 37, \quad 123 - 62 = 61, \quad 214 - 123 = 91, \quad 341 - 214 = 127.25 − 6 = 19 , 62 − 25 = 37 , 123 − 62 = 61 , 214 − 123 = 91 , 341 − 214 = 127Observe the pattern of differences:
The differences are: 19,37,61,91,12719, 37, 61, 91, 12719, 37 ,61 ,91 , 127.
These are increasing, and they approximately follow the pattern of +18,+24,+30,+36+18, +24, +30, +36+18,+24,+30,+36, indicating increasing differences.Find the next difference:
The next difference should be 127+42=169127 + 42 = 169127 + 42 = 169 (increase by 42, following the pattern of incrementing by 6).Calculate the next term:
341+169=510.341 + 169 = 510.341 + 169 = 510
Add this difference to the last term in the sequence:
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