7
6. In a geometric sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\)
- the common ratio is \(r\)
- \(u _ { 2 } + u _ { 3 } = 6\)
- \(u _ { 4 } = 8\)
- Show that \(r\) satisfies
$$3 r ^ { 2 } - 4 r - 4 = 0$$
Given that the geometric sequence has a sum to infinity,
find \(u _ { 1 }\)find \(S _ { \infty }\)
7.
$$f ( x ) = A x ^ { 3 } + 6 x ^ { 2 } - 4 x + B$$
where \(A\) and \(B\) are constants.
Given that
- ( \(x + 2\) ) is a factor of \(\mathrm { f } ( x )\)
- \(\int _ { 3 } ^ { 5 } \mathrm { f } ( x ) \mathrm { d } x = 176\)
find the value of \(A\) and the value of \(B\).