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Type the missing number in this sequence:\newline75,  80,  85,  90,  ____,  100,  10575,\;80,\;85,\;90,\;\_\_\_\_,\;100,\;105

Full solution

Q. Type the missing number in this sequence:\newline75,  80,  85,  90,  ____,  100,  10575,\;80,\;85,\;90,\;\_\_\_\_,\;100,\;105
  1. Observe pattern: We observe the sequence to determine the pattern. The numbers are increasing by a constant difference.
  2. Calculate differences: We calculate the difference between consecutive terms in the sequence. The difference between 8080 and 7575 is 55, and the difference between 8585 and 8080 is also 55.
  3. Apply difference to find missing number: We apply the same difference to find the missing number. Since the difference is 55, we add 55 to the last known number before the missing number, which is 9090.\newline90+5=9590 + 5 = 95
  4. Check result: We check if adding 55 to the missing number gives us the next number in the sequence. Adding 55 to 9595 should give us 100100.\newline95+5=10095 + 5 = 100

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