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# a quadratic sequence has the first three terms 5 13 and 25. find the nth term of the sequence?

how do i do this? everytime i try i get it wrong. online class is not helping

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- sepiaLv 71 month ago
The nth term is an² + bn + c

The first three terms 5, 13, and 25.

a + b + c = 5

4a + 2b + c = 13

9a + 3b + c = 25

Solution:

a = 2, b = 2, c = 1

The nth term is 2n² + 2n + 1

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- Wayne DeguManLv 71 month ago
The nth term is an² + bn + c

When n = 1 we have a value of 5 so,

a + b + c = 5....(1)

With n = 2 we have 13 so,

4a + 2b + c = 13...(2)

And with n = 3 we have:

9a + 3b + c = 25...(3)

(2) - (1) => 3a + b = 8...(4)

(3) - (2) => 5a + b = 12...(5)

(5) - (4) => 2a = 4

Hence, a = 2

Then, b = 2 => c = 1

Therefore, nth term is 2n² + 2n + 1

This checks out for n = 1, 2 and 3

:)>

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