You may notice that the numbers are one more than the triangular numbers. So
t(n) = n(n + 1)/2 + 1 for n = 1, 2, 3, ...
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One rule for this pattern is to add twice the previous value added 4 + 1 = 5 5 + 2×1 = 5 + 2 = 7 7 + 2×2 = 7 + 4 = 11 11 + 2×4 = 11 + 8 = 19 Continuing the next numbers would be: 19 + 2×8 = 19 + 16 = 35 35 + 2×16 = 35 + 32 = 67 ...
Everytime you move to the next number you add 1, then 2, then 3, etc.1+1=22+2=44+3=77+4=1111+5=1616+6=2222+7=2929+8=37
f(x) = -4x2 - 16x - 11 a = -4, b = -16, c = -11 x-coordinate of the vertex = -b/2a = -(-16)/2(-4) = 16/-8 = -2 y-coordinate = f(-2) = -4(-2)2 -16(-2) - 11 = -16 + 32 - 11 = 5 vertex is (-2, 5)
29 because 1+1=2 2+2=4 4+3=7 7+4=11 11+5=16 16+6=22 22+7=29
Divide by 2 to get the next term.