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1, 2, 5, 10, 17, 26, ?
What is the next number in this pattern and what are the two ways of working it out?
1, 2, 5, 10, 17, 26, ?
1, 2, 5, 10, 17, 26, ?
Answer
37.The first way of working it out is to square each number in order (0, 1, 2, 3, 4, 5) and each time, add one.
The second way is to add each odd number in order (1, 3, 5, 7, 9) to the previous term.
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Comments
Please can you explain the second way again. I don't understand it. Thanks.
The first way is incorrect. If you square 1 and add 1 you get 2 etc. Here is a method that works. n^2 - 2n + 2 so the sixth term is 6^2 -12 + 2 = 36 - 12 + 2 = 26. A second way is to start with 1 skip 0 and get 2, skip 2 (3 and 4) and get 5, skip 4 (6,7,8,9) and get 10 and so on skipping over 2 more numbers each time. So 26 skip 10 get 37.
The first method will work if you start from zero. Thus 0^2 + 1 = 1, 1^2 + 1 = 2 etc.
okay, jimbos first comment, second part - you explained what he meant by adding increasing numbers...
also, while these seem like two unrelated ways to do this problem, the second answer is actually based on the fact of the first answer (except the adding 1 part) - different between 0^2 and 1^2 = 1, 1^2 and 2^2 = 3, 2^2 and 3^2 = 5, so its 1,3,5,7,9,11,13, etc. the reason for this is that when comparing a square to the previous numbers square - take the square, then add 2 times the number then 1 (to see it mathematically, think of (x+1)^2 = (x^2 +2x+1)
also, while these seem like two unrelated ways to do this problem, the second answer is actually based on the fact of the first answer (except the adding 1 part) - different between 0^2 and 1^2 = 1, 1^2 and 2^2 = 3, 2^2 and 3^2 = 5, so its 1,3,5,7,9,11,13, etc. the reason for this is that when comparing a square to the previous numbers square - take the square, then add 2 times the number then 1 (to see it mathematically, think of (x+1)^2 = (x^2 +2x+1)
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