An arithmetic progression has first term 5 and common difference $$\(d\)$$, where $$\(d> 0\)$$. The second, fifth and eleventh terms of the arithmetic progression, in that order, are the first three terms of a geometric progression. The sum of the first 77 terms of the arithmetic progression is denoted by $$\(S_{77}\)$$. The sum of the first 10 terms of the geometric progression is denoted by $$\(G_{10}\)$$. $$\[ \text { Find the value of } S_{77}-G_{10} \text {. } \]$$ ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . 11 The function f is defined by $$\(\mathrm{f}(x)=3+6 x-2 x^{2}\)$$ for $$\(x \in \mathbb{R}\)$$. (a) Express $$\(\mathrm{f}(x)\)$$ in the form $$\(a-b(x-c)^{2}\)$$, where $$\(a, b\)$$ and $$\(c\)$$ are constants, and state the range of $$\(f\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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