We need to write system of equations for this problem. Reading text we write 1 equation by 1.
first lets name our variables
x - Kiana cards
y - Gary cards
z - Monty cards
m - Willa cards
x = y-3 which we can write as y = x+3
z = x + 7
m = 2z
x + y + z + m = 74
I think easiest way to solve this is to express all variables in last equation and solve for x.
x + x+3 + x + 7+ 2x + 14= 74
5x = 50
x = 10
now we just calculate cards given to each friend
y = 13
z = 17
m = 34
To solve this, we would need to figure out the values of 
for which an absolute value is negative. From basics, you should know that an absolute value is always greater than or equal to 0.
If we rearrange this equation a little bit, we get,
So 
<em>cannot </em>be negative. So,
For this to <em>have </em>a solution, k needs to be greater than or equal to 
.
For <em>no solution</em>, k is less than -5. So, values of k which will make the equation to <em>not </em>have any solution is 
.
ANSWER:
The next terms in the sequence will be multiplied by c, but the common ratio is still the same
example :
S = [1(3)^4 - 1]/ [3-1] = 80/2 - 40
Hope this helps
