Determine the pattern and find the missing terms in each of the following:

2,5,10,17, , 65, , 145, , ,?

Answer:Pattern: start at 2 and add consecutive odd numbers: +3, +5, +7, +9, +11, +13, +15, …(That is the same as the formula term n: n² + 1.)Work out the sequence (add the odd numbers step by step):22 + 3 = 55 + 5 = 1010 + 7 = 1717 + 9 = 2626 + 11 = 3737 + 13 = 5050 + 15 = 6565 + 17 = 8282 + 19 = 101101 + 21 = 122122 + 23 = 145… and so on.Completed sequence (first 12 terms):2, 5, 10, 17, 26, 37, 50, 65, 82, 101, 122, 145So the missing terms (to fill the blanks between the given numbers) are:after 17 → 26, 37, 50 (these come before 65)after 65 → 82, 101, 122 (these come before 145)You can also check each term with the formula n² + 1:1²+1 = 2, 2²+1 = 5, 3²+1 = 10, 4²+1 = 17, 5²+1 = 26, … 12²+1 = 145.Step-by-step explanation:have a nice day, kindly brainliest ;⁠)

Answered by miraekiru | 2025-08-25