The sequence: 55 176 539 1628

Question

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

Answer 1

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.