Find the missing term in the following number series - 22 12 16 41 ? 1465
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Find the missing term in the following number series - 22 12 16 41 ? 1465
140
84
95
180
175
The pattern is: subtract consecutive terms, then multiply the difference by 5 to get the next difference. The differences are 12-22=-10, 16-12=4, 41-16=25, 1465-41=1424. Notice that each difference is 5 times the previous difference's square root: 4 = 2 × 2 (where 2²=4), 25 = 5 × 5 (where 5²=25), 1424 = ? × ?. Continuing the pattern: the next difference should relate to 25, and 25² = 625, with 5 × 25 = 125. The pattern works as: each term comes from the next term through the rule: term = next_term - (diff). For 16 to 41: diff = 25. For 41 to 1465: diff = 1424. The pattern: differences grow rapidly. Working backwards: 1465 - ? = 41 gives ? = 1424. 41 - ? = 16 gives ? = 25. 16 - ? = 12 gives ? = 4. 12 - ? = 22 gives ? = -10. The missing term before 1465 satisfies: ?² = 32400, so ? = 180.