The rule is 5, 10, 15 and so the next number will be 20+31 = 51
You double the number before it and add 1.
multiplication pattern
The pattern at each stage is the addition of a square number of increasing value to the previous term. 1 + 12 = 2 2 + 22 = 6 6 + 32 = 15 15 + 42 = 31 31 + 52 = 56 56 + 62 = 92 The formula for the nth term is, a(n) = n3/3 + n2/2 + n/6 + 1 or it can be written a(n) = 1/6(2n3 + 3n2 + n + 6) So the 7th term = 1/6(686 + 147 + 7 + 6) = 1/6 x 846 = 141 ( = 92 + 72) NOTE : The rule is the same as the sum of the squared numbers plus one. So another way of presenting the formula is, a(n) = 1/6[n(n + 1)(2n + 1)] + 1
15+15+1=31
The rule is 5, 10, 15 and so the next number will be 20+31 = 51
Add 3 each time
You double the number before it and add 1.
multiplication pattern
The gaps are 5, 10, 15, 20, ..... The rule becomes add 5(n-1) to the previous number So that the second number is found by adding 5 times (2-1) to 1 = 5+1 = 6 and the third number is found by adding 5 times (3-1) to 6 = 10+6 = 16 and the fourth number is found by adding 5 times (4-1) to 16 = 15+15 = 31 and so on....
One possible rule is: Un = (219n5 - 3755n4 + 24075n3 - 70645n2 + 92166n - 36960)/120 for n = 1, 2, 3, etc
The pattern at each stage is the addition of a square number of increasing value to the previous term. 1 + 12 = 2 2 + 22 = 6 6 + 32 = 15 15 + 42 = 31 31 + 52 = 56 56 + 62 = 92 The formula for the nth term is, a(n) = n3/3 + n2/2 + n/6 + 1 or it can be written a(n) = 1/6(2n3 + 3n2 + n + 6) So the 7th term = 1/6(686 + 147 + 7 + 6) = 1/6 x 846 = 141 ( = 92 + 72) NOTE : The rule is the same as the sum of the squared numbers plus one. So another way of presenting the formula is, a(n) = 1/6[n(n + 1)(2n + 1)] + 1
Start at 1. Multiply by 3. Subtract 1. Multiply by 3. Subtract 1. Repeat this pattern.
The rule of this pattern is obfuscated by the omission of spaces, giving the impression that this is the number "111,359,173,157". However, the underlying pattern follows the function of the Fibonacci series, but adding sets of 3 instead of sets of 2. So, 1+1+1=3, 1+1+3=5, 1+3+5=9, 3+5+9=17, 5+9+17=31, 9+17+31=57.
15+15+1=31
Each successive number is the sum of the previous number times 2, plus 1.
It is 15.5 or 15 and a half.