Which number will replace the question mark (?) in the following series?
68, 67, ?, 65, 72, 63
- A79
- B80
- C55
- D70
Solution & Step-by-step Explanation
Let's examine the differences between alternate terms or consecutive terms:
Let's look at the consecutive differences:
67−68=−1
?−67=x
65−?=y
72−65=+7
63−72=−9
Notice the pattern at the end: +7,−9. This looks like an alternating sequence of increasing odd numbers with alternating signs: −1,+3,−5,+7,−9.
Let's test this pattern hypothesis:
68−1=67
67+3=70 (So ?=70)
70−5=65 (Matches the next term!)
65+7=72 (Matches!)
72−9=63 (Matches!)
Thus, the missing number is 70.
Let's look at the consecutive differences:
67−68=−1
?−67=x
65−?=y
72−65=+7
63−72=−9
Notice the pattern at the end: +7,−9. This looks like an alternating sequence of increasing odd numbers with alternating signs: −1,+3,−5,+7,−9.
Let's test this pattern hypothesis:
68−1=67
67+3=70 (So ?=70)
70−5=65 (Matches the next term!)
65+7=72 (Matches!)
72−9=63 (Matches!)
Thus, the missing number is 70.