Question

what would be the 12th term for 7,14,25,40,59

Answer 1

Answer:

How do I solve this quadratic sequence: 4, 7, 14, 25, 40 with an2 + bn + c?

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Paulina Jonušaitė

Answered 4 years ago

How do I solve this quadratic sequence: 4, 7, 14, 25, 40 with an2 + bn + c?

Okay, so for n=1 you get 4, for n=2 you get 7, and for n=3 you get 14. That’s all you need to completely define a quadratic sequence!

⎧⎩⎨a×12+b×1+c=4a×22+b×2+c=7a×32+b×3+c=14

This is a system of linear equation in respect of a, b and c, and you can use whatever is your favourite method to solve it. You get the following solution.

⎧⎩⎨a=2b=−3c=5

xn=2×n2−3×n+5

Indeed, when you plug in 4, you get

2×16−3×4+5=32−12+5=25

and when you plug in 5, you get

2×25−3×5+5=50−15+5=40