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....
Start by adding 7, then add 7x2, then 7x4, then 7x8, etc. 2 + (7x1) = 9 9 + (7x2) = 23 23 + (7x4) = 51 51 + (7x8) = 107 The next number is 219.
The consecutive integers whose sum is 51 are 16, 17, and 18.
Let the numbers be 'm' & 'n' Hence mn = 51 (Multiplication) m + n = -16 (Addition) Algebraically rearrange m = -16 -n Ssubstitute (-16-n) n = 51 -16n - n^2 = 51 n^(2) + 16n + 51 = 0 ( It is now in Quadratic form to solve). Complete the Square (n + 8)^2 - 8^(2) = -51 (n + 8)^2 = -51 + 64 = 13 Square root both sides n + 8 = +/-sqrt(13) n + 8 = +/- 3.60555.... n = -13.60555.... & -4.39444.... Are the two number.
The integers are 16, 17 and 18.
Four examples of irrational numbers are 21/2, 31/2, 51/2 & 71/3
The rule is 5, 10, 15 and so the next number will be 20+31 = 51
The rule is 5 10 15 20 25 30 .... etc and accordingly the next number in the sequence will be 106
Alternating terms form the same pattern16 +5 = 2126 + 5 = 31Odd terms would then be 16, 21, 26, 31, 36, 41Even terms would be 26, 31, 36, 41, 46, 51Putting them together16, 26, 21, 31, 26, 36, 31, 41, 36, 46, 41, 51, ...
31 is prime, but 51 is not as 51=3*17.
The LCM of 31 and 51 is 1,581.
r=5>7}2
31/51 is in its simplest form.
Dissolving into prime divisors we get 16 = 24 14 = 21 * 71 12 = 22 * 31 10 = 21 * 51 8 = 23 6 = 21 * 31 Taking the greatest exponents for each prime, we get lcm(16,14,12,10,8,6) = 24 * 31 * 51 * 71 = 1680
51-16 = 35
51/6 + 26/9 = 51/6 + 22/3 = 31/6 + 8/3 = 31/6 + 16/6 = 47/6 = 75/6
gcf(16, 51) = 1 lcm(16, 51) = 816
Start by adding 7, then add 7x2, then 7x4, then 7x8, etc. 2 + (7x1) = 9 9 + (7x2) = 23 23 + (7x4) = 51 51 + (7x8) = 107 The next number is 219.