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Select the number from among the given options that can replace the question mark (?) in the following series: 26, 78, 36, 108, 66, 198,?
128
164
142
156
156
Identify the alternating two-step pattern: multiply by 3, then subtract a number or follow the dual sequence 26->36->66->(?), 78->108->198->(?). Alternately, look at consecutive operations: multiply by 3, add 10, multiply by 3, subtract 40... Or more simply: 26 x 3 = 78, 78 - 42 = 36, 36 x 3 = 108, 108 - 42 = 66, 66 x 3 = 198, 198 - 42 = 156.
Identify the alternating two-step pattern: multiply by 3, then subtract a number or follow the dual sequence 26->36->66->(?), 78->108->198->(?). Alternately, look at consecutive operations: multiply by 3, add 10, multiply by 3, subtract 40... Or more simply: 26 x 3 = 78, 78 - 42 = 36, 36 x 3 = 108, 108 - 42 = 66, 66 x 3 = 198, 198 - 42 = 156.
Step 1: Analyze consecutive pairs
Examine the relationship between adjacent numbers: 26 to 78 is multiplied by 3 (26 x 3 = 78).
Step 2: Check next transition
From 78 to 36, subtract 42 (78 - 42 = 36).
Step 3: Verify the alternating rule
The pattern continues as (x 3) followed by (- 42): 36 x 3 = 108, 108 - 42 = 66, and 66 x 3 = 198.
Step 4: Find the missing term
Applying the next operation (- 42) to 198 gives: 198 - 42 = 156.
A: 128 is incorrect because the calculated missing number is 156. B: 164 is incorrect because it does not follow the alternating (x3, -42) pattern. C: 142 is incorrect as the arithmetic sequence yields 156.
D is correct because applying the alternating pattern of multiplying by 3 and subtracting 42 to the last term 198 results in 198 - 42 = 156.
When numbers fluctuate up and down or grow rapidly then drop slightly, always check for alternating two-step operations such as (x, -) or (+, x).
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