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Which of the following numbers will replace the question mark (?) in the given series? 225, 200, 183, 174, ?, 168
170
168
167
169
169
Calculate the differences between consecutive terms to identify a decreasing secondary series involving the sum of digits of the preceding number.
Calculate the differences between consecutive terms to identify a decreasing secondary series involving the sum of digits of the preceding number.
Analyze consecutive differences
Find the difference between each term: 225 - 200 = 25; 200 - 183 = 17; 183 - 174 = 9. The differences are 25, 17, 9.
Identify the pattern of differences
Observe the relationship: 25 - 8 = 17; 17 - 8 = 9. The differences are decreasing by 8 each time. Therefore, the next difference should be 9 - 8 = 1.
Calculate the missing term
Apply the next difference to the last known term: 174 - 5 = 169 (Wait: let's re-evaluate). Correction: If the difference pattern is 25, 17, 9, 5, 1... 174 - 5 = 169. Then 169 - 1 = 168. This confirms the sequence.
A: 170 is incorrect as 174 - 170 = 4, which does not fit the sequence; B: 168 is the next term after the missing one; C: 167 is incorrect as 174 - 167 = 7, which deviates from the required difference of 5.
D is correct because the series follows a pattern of subtracting decreasing values (25, 17, 9, 5, 1), leading to 174 - 5 = 169.
When consecutive differences don't show an obvious pattern immediately, look for the 'second-order difference' by subtracting the differences themselves.
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