What number would replace questions mark (?) in the series given below?
2, 5, 10, 19, 36, 69, 134?
263
The series is: 2, 5, 10, 19, 36, 69, 134, ?
Step 1: Find the differences between consecutive terms.
5−2 = 3
10−5 = 5
19−10 = 9
36−19 = 17
69−36 = 33
134−69 = 65
Step 2: Look at the pattern in these differences: 3, 5, 9, 17, 33, 65
Notice that each difference is obtained by doubling the previous difference and subtracting 1:
2×3−1 = 5
2×5−1 = 9
2×9−1 = 17
2×17−1 = 33
2×33−1 = 65
Step 3: Find the next difference using the same rule.
Next difference = 2×65−1 = 129
Step 4: Add this difference to the last term of the series.
? = 134 + 129 = 263
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