#MAASL00266

a) Use the geometric sequence formula: u_{n}=u_{1}r^{n-1}

Find unknown variable: r

Find the common ratio by dividing two consecutive terms: \frac{9}{3}=3 ; r=3

Plug in 18 for n ; and 3 as u_{1}

Substitute back into formula:

u_{18}=3(3)^{18-1}

u_{18}=387420489



b) Substitute into the geometric sequence formula:

u_{n}=1594323 ; r=3 ; u_{1}=3

u_{n}=u_{1}r^{n-1}

1594323=3(3)^{n-1}

531441=3^{n-1}

Use logarithms to find the unknown exponents

log_{3}(531441)=n-1

12=n-1

n=13

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