Question 1108399
general form of quadratic sequence is
:
an^2 + bn + c, where a,b,c are real numbers
:
for n=1, a + b + c = -3
for n=2, 4a + 2b + c = -2
for n=3, 9a + 3b + c = x
for n=4, 16a + 4b + c = -6
for n=5, 25a + 5b + c = y
:
we will use the following 3 equations with 3 unknowns
:
a + b + c = -3
4a + 2b + c = -2
16a + 4b + c = -6
:
use any linear equation solver for 3 equations with 3 unknows
:
a = -1, b = 4, c = -6
:
the equation for the nth term is
:
-n^2 +4b -6
:
for n = 1, we have -1 +4 -6 = -3
for n = 2, we have -4 +8 -6 = -2
for n = 3, we have -9 +12 -6 = -3
for n = 4, we have -16 +16 -6 = -6
for n = 5, we have -25 +20 -6 = -11
:
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x = -3 and y = -11
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