Select the number from among the given options that can replace the question mark (?) in the following series.
62, 74, 80, 86, 95, ?, 158

The correct answer is 113.

To find the missing number, we first calculate the differences between consecutive terms in the series:

62  →  74  →  80  →  86  →  95  →  ?  →  158

Differences:
74 - 62 = 12
80 - 74 = 6
86 - 80 = 6
95 - 86 = 9
? - 95 = d₅
158 - ? = d₆

So the sequence of differences so far is: 12, 6, 6, 9, d₅, d₆

Now, let's examine the ratios of consecutive differences (i.e., how each difference relates to the one before it):

6 ÷ 12 = 0.5
6 ÷ 6 = 1.0
9 ÷ 6 = 1.5
d₅ ÷ 9 = 2.0   (following the pattern)
d₆ ÷ d₅ = 2.5   (following the pattern)

The ratios form a clear arithmetic progression: 0.5, 1.0, 1.5, 2.0, 2.5, ... — increasing by 0.5 each time.

Using this pattern to find the missing differences:

d₅ = 9 × 2.0 = 18
d₆ = 18 × 2.5 = 45

Now we can verify:

? = 95 + 18 = 113
158 = 113 + 45 = 158 ✓

The complete series with all differences verified:

62  (+12)  74  (+6)  80  (+6)  86  (+9)  95  (+18)  113  (+45)  158

Therefore, the missing number that replaces the question mark is 113.