The sequence: 55 176 539 1628
in the sequence above each term after the first is determined by multiplying by x and then adding y if x and y are each greater than zero and if they are integers then what does the term x+y equal
To find the value of x + y, we need to determine the values of x and y from the given sequence.
Let's observe the differences between consecutive terms:
176 - 55 = 121
539 - 176 = 363
1628 - 539 = 1089
We can see that the differences are perfect squares: 121 = 11^2, 363 = 19^2, and 1089 = 33^2.
Therefore, we can deduce that x = the square root of each difference: x = 11, x = 19, x = 33.
Now that we know x, we can substitute it back into the second term to find y:
176 = 55x + y
176 = 55(11) + y
176 = 605 + y
y = -429
For the third term:
539 = 176x - 429
539 = 176(19) - 429
539 = 3404 - 429
y = -3065
For the fourth term:
1628 = 539x - 3065
1628 = 539(33) - 3065
1628 = 17787 - 3065
y = 14722
Finally, we can find the value of x + y by adding x and y from the fourth term:
x + y = 33 + 14722
x + y = 14755
Therefore, x + y = 14755.
To find the value of x+y, we can look at the pattern in the given sequence. Notice that each term after the first is obtained by multiplying the previous term by x and then adding y.
Let's analyze the given sequence step by step:
Term 1: 55
Term 2: 55 * x + y (unknown)
Term 3: (55 * x + y) * x + y = 55 * x^2 + x*y + y (unknown)
Term 4: ((55 * x^2 + x*y + y) * x + y) = 55 * x^3 + x^2 * y + x * y + y (unknown)
From the given sequence, we can see that the terms are getting larger, indicating that x and y are positive integers. Now, let's compare the terms to figure out x and y:
Term 1: 55
Term 2: 176 = 55 * x + y
Term 3: 539 = 55 * x^2 + x * y + y
Term 4: 1628 = 55 * x^3 + x^2 * y + x * y + y
Since x and y are integers, we need to find values for x and y that satisfy all the equations simultaneously.
Using trial and error, we can find that x = 3 and y = 11 satisfy all the equations:
Term 1: 55
Term 2: 55 * 3 + 11 = 176
Term 3: 55 * 3^2 + 3 * 11 + 11 = 539
Term 4: 55 * 3^3 + 3^2 * 11 + 3 * 11 + 11 = 1628
Therefore, x + y = 3 + 11 = 14.
To find the value of x+y, we need to analyze the pattern in the given sequence: 55, 176, 539, 1628.
Let's break down the pattern step by step to understand how each term is generated.
The first term, 55, is given as it is.
To obtain the second term, 176, we multiply the first term by x and then add y. Let's represent this as an equation: 55x + y = 176.
For the third term, 539, we apply the same logic: 176x + y = 539.
Finally, for the fourth term, 1628, we have: 539x + y = 1628.
Now we have a system of three equations with two unknowns (x and y). We can solve this system of equations to find the values of x and y, which will allow us to determine the value of x+y.
Let's solve the system of equations:
Equation 1: 55x + y = 176
Equation 2: 176x + y = 539
Equation 3: 539x + y = 1628
There are different methods to solve this system, such as elimination, substitution, or matrices. I will use the elimination method here.
Subtracting Equation 1 from Equation 2, we get:
(176x + y) - (55x + y) = 539 - 176
121x = 363
x = 363 / 121
x = 3
Now, substitute this value of x into any of the original equations to solve for y. Let's use Equation 1:
55(3) + y = 176
165 + y = 176
y = 176 - 165
y = 11
Therefore, x = 3 and y = 11.
To find the value of x+y:
x + y = 3 + 11 = 14.
Hence, the term x+y equals 14.