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a) u_{6}=20(\frac{1}{2})^{6-1}

u_{6} = 0.625



b) S_{n}= \frac{a_{1}}{1-r}

S_{n}= \frac{20}{1-0.5}

S_{n}= \frac{20}{0.5}

S_{n} = 40



c) a_{n}=a_{1}+(n-1)(d)

a_{8}=-18+(8-1)(d)

-4=-18+(7)(d)

14=7d

d=2



d) a_{n} = a_{1} + (n-1)d

a_{n} = -18 + (n-1)2

a_{n} = -20 + 2n

Substitute into sum of arithmetic sequence formula

S_{n}=\frac{n}{2}(a_{1}+a_{n})

S_{n}=\frac{n}{2}(-18+(-20+2n))

S_{n}=\frac{n}{2}(-38+2n)

S_{n}=\frac{n}{2}2(-19+n)

S_{n}=n(-19+n)

S_{n}=-19n+n^{2}



e) 40 = 2(-19n+n^{2})

0 = n^{2} - 19n - 20

n=-1, n=20

Discard the negative n as it is not possible to have a negative number

n=20

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