# How to find the value of $h(99)$ in the function?

If $$h(x) + h(x+1) = 2x^2$$ and $$h(33) = 99$$ What will be the value of $h(99)$?

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$h(33)+h(34)=2*33^2$ so $h(34)=...$. Then, continue for $f(35)$ and so on, try to find a logic behind it and you'll get $h(99)$ quite fast. –  barto Jan 26 '13 at 19:34

$$h(34)=2\times 33^2-h(33)$$ $$h(35)=2\times 34^2-h(34)=2\times 34^2-2\times 33^2+h(33)$$ $$\dots$$ $$h(99)=2\times 98^2 - 2\times 97^2 + 2\times 96^2 -\cdots + 2\times 34^2 - 2\times 33^2 +h(33)\\=2(98^2-97^2+96^2-\cdots+34^2-33^2)+99\\ =2(98+97+\cdots +34+33)+99\\ =8745$$