For each of these lists of integers, provide a simple formula orrule that generates the terms of an integer sequence that beginswith the given list. assuming that your formula or rule is correct, determine the next three terms of the sequence. a)3,6,11,18,27,38,51,66,83,
b) 7, 11, 15, 19, 23, 27, 31, 35, 39, 43,
c) 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010,
d) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5,
f) 1, 3, 15, 105, 945, 10395, 135135, 2027025,
g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,

The next three terms for each are: a) 123, 146, 171; b) 47,51,55; c) 10000,10001, 10010; d)8,8,8; f)654729075,13749310575,316234142225; g)0,0,0

Step-by-step explanation:

In a) the last number +(2i+1) in which i is the number of terms=1,2,3...

b) n+4, for any last number, you add 4

c) 1,0 and the same is repeated for the next decimal

d) n=sum of 2 previous different numbers. The frequency is given by 2i-1 in which is is the number of terms i=1,2,3...

e) missing

f) ni+1=n*(2i-1) in which ni+1 is the resulting number, n is the previous number and i is the number of terms=1,2,3...

g) it is 1 for odd numbers and 0 for even numbers. The frequency is given by i+1, in which the number of terms i= 0,1,2,3...

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1