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Type the missing number in this sequence:\newline3,  5,  9,  15,  23,  ____,  45,  593,\;5,\;9,\;15,\;23,\;\_\_\_\_,\;45,\;59

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Full solution

Q. Type the missing number in this sequence:\newline3,  5,  9,  15,  23,  ____,  45,  593,\;5,\;9,\;15,\;23,\;\_\_\_\_,\;45,\;59
  1. Identify Pattern: 3,5,9,15,23,_,45,593, 5, 9, 15, 23, \_, 45, 59\newlineIdentify the pattern in the sequence.\newlineLook at the differences between consecutive terms.
  2. Calculate Differences: Calculate the differences between consecutive terms.\newline5−3=25 - 3 = 2\newline9−5=49 - 5 = 4\newline15−9=615 - 9 = 6\newline23−15=823 - 15 = 8\newlineNotice that the differences are increasing by 22 each time.
  3. Predict Next Difference: Predict the next difference in the pattern.\newlineSince the last difference we calculated was 88, the next difference should be 8+2=108 + 2 = 10.
  4. Find Missing Number: Add the predicted difference to the last known term to find the missing number. 23+10=3323 + 10 = 33 The missing number should be 3333.
  5. Verify Sequence: Verify the pattern continues correctly after the missing number. 33+(10+2)=33+12=4533 + (10 + 2) = 33 + 12 = 45 The sequence continues correctly, so our missing number is confirmed.

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