Question

determine the next three numbers in this pattern:
2,3,5,7,11,13,17,19,23,___,___,___


Aren't these all prime numbers?


Find the next three numbers in the pattern. 5,2,-1,-4
3,2,0,-3,-7
-8,-6,-2,4,12
-5,-7,-8,-10,-11

Answer 1

The first pattern looks like all primes, so the next numbers in the sequence would be

29, 31, 37

______________
5, 2, -1, -4

You subtract three to get the next number, so the next three numbers would be
-7, -10, -13
______________
3, 2, 0, -3, -7

To get the second term, you subtract 1 (3-1 = 2)
To get the third term, you subtract 2 from the 2nd term (2-2 = 0)
. . . To get the (n+1)th term you subtract n-1 from the nth term

The next numbers would be -12, -18, -25
______________________
-8, -6, -2, 4, 12

To get second term, you add 2 to the first term;
To get the third term, you add 4 to the second term;
To get the (n+1)th term, you add (n-1)*2 to the nth term
The next terms in the sequence are
12 + 8, 12 + 8 + 10, 12 + 8 + 10 + 12
= 20, 30, 42

__________________
-5, -7, -8, -10, -11

This looks like you alternating between adding -2 and -1; The next three terms would be

-13, -14, -16

Answer 2

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