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chelly70
24.01.2021 •
Mathematics
Here are the first four terms of a quadratic sequence.
The nth term of this sequence is an² + bn + c.
1, 11, 27 and 49
Find the values of a, b and c.
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Ответ:
a = 3, b = 1, c = - 3
Step-by-step explanation:
Substitute n = 1, 2, 3 into the n th term
a + b + c = 1 → (1)
4a + 2b + c = 11 → (2)
9a + 3b + c = 27 → (3)
Subtract (1) from (2) term by term to eliminate c
Subtract (2) from (3) term by term to eliminate c
3a + b = 10 → (4)
5a + b = 16 → (5)
Subtract (4) from (5) term by term to eliminate b
2a = 6 ( divide both sides by 2 )
a = 3
Substitute a = 3 into (4) and evaluate for b
3(3) + b = 10
9 + b = 10 ( subtract 9 from both sides )
b = 1
Substitute a = 3, b = 1 into (1) and evaluate for c
3 + 1 + c = 1
4 + c = 1 ( subtract 4 from both sides )
c = - 3
Then a = 3, b = 1 and c = - 3
Ответ:
Answer is in the photo. I couldn't attach it here, but uploaded it to a file hosting. link below! Good Luck!
cutt.ly/4zZs6GM