Given two terms in a geometric sequence find the common ratio.
14) $a_3 = 144$ and $a_6 = 31104$
15) $a_6 = 2048$ and $a_1 = 2$
16) $a_3 = -50$ and $a_2 = 10$
Evaluate each geometric series described.
17) $\sum_{n=1}^{8} 2^{n-1}$
18) $4 - 12 + 36 - 108..., n=9$
19) $a_1 = 2, a_n = 1024, r = 2$
20) $a_1 = -2, r = -3, n = 7$
Determine the number of terms $n$ in each geometric series.
21) $3 + 9 + 27 + 81..., S_n = 3279$
22) $\sum_{i=1}^{n} -2 \cdot (-5)^{i-1} = 208$
Determine the common ratio of the infinite geometric series.
23) $a_1 = -2, S = -\frac{5}{2}$
Evaluate each infinite geometric series described.
24) $a_1 = 1, r = -\frac{1}{5}$
25) $-6 - \frac{6}{5} - \frac{6}{25} - \frac{6}{125}...$
26) $\sum_{m=1}^{\infty} -160 \cdot \left(-\frac{1}{2}\right)^{m-1}$
Express as a fraction in lowest terms. SHOW ALL WORK!
27) $0.2626262626...$ (repeating)
28) $-2.075075075$ (repeating)
