Answer:
1. 786432
2. 15/32
3. 1/6561
4. 236196
5. -12288
Step-by-step explanation:
[tex]\mathrm{1.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{10} = 3\cdot (4)^{10-1}}\\\\\mathrm{a_{10} = 3\cdot (4)^{9}}\\\\\mathrm{a_{10} = 3\cdot 262144}\\\\\mathrm{a_{10} = 786432}[/tex]
[tex]\mathrm{2.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{9} = 120\cdot (\frac{1}{2} )^{9-1}}\\\\\mathrm{a_{9} = 120\cdot (\frac{1}{2})^{8}}\\\\\mathrm{a_{9} = 120\cdot \frac{1}{256} }\\\\\mathrm{a_{9} = \frac{15}{32} }[/tex]
[tex]\mathrm{3.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{12} = 27\cdot (\frac{1}{2} )^{12-1}}\\\\\mathrm{a_{12} = 27\cdot (\frac{1}{2})^{11}}\\\\\mathrm{a_{12} = 27\cdot \frac{1}{177147} }\\\\\mathrm{a_{12} = \frac{1}{6561} }[/tex]
[tex]\mathrm{4.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{11} = 4\cdot (3)^{11-1}}\\\\\mathrm{a_{11} = 4\cdot (3)^{10}}\\\\\mathrm{a_{11} = 4\cdot 59049}\\\\\mathrm{a_{11} = 236196}[/tex]
[tex]\mathrm{5.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{13} = -3\cdot (-2)^{13-1}}\\\\\mathrm{a_{13} = -3\cdot (-2)^{12}}\\\\\mathrm{a_{13} = -3\cdot 4096}\\\\\mathrm{a_{13} = -12288}[/tex]
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Answers & Comments
Answer:
1. 786432
2. 15/32
3. 1/6561
4. 236196
5. -12288
Step-by-step explanation:
[tex]\mathrm{1.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{10} = 3\cdot (4)^{10-1}}\\\\\mathrm{a_{10} = 3\cdot (4)^{9}}\\\\\mathrm{a_{10} = 3\cdot 262144}\\\\\mathrm{a_{10} = 786432}[/tex]
[tex]\mathrm{2.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{9} = 120\cdot (\frac{1}{2} )^{9-1}}\\\\\mathrm{a_{9} = 120\cdot (\frac{1}{2})^{8}}\\\\\mathrm{a_{9} = 120\cdot \frac{1}{256} }\\\\\mathrm{a_{9} = \frac{15}{32} }[/tex]
[tex]\mathrm{3.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{12} = 27\cdot (\frac{1}{2} )^{12-1}}\\\\\mathrm{a_{12} = 27\cdot (\frac{1}{2})^{11}}\\\\\mathrm{a_{12} = 27\cdot \frac{1}{177147} }\\\\\mathrm{a_{12} = \frac{1}{6561} }[/tex]
[tex]\mathrm{4.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{11} = 4\cdot (3)^{11-1}}\\\\\mathrm{a_{11} = 4\cdot (3)^{10}}\\\\\mathrm{a_{11} = 4\cdot 59049}\\\\\mathrm{a_{11} = 236196}[/tex]
[tex]\mathrm{5.\: a_n = a_1\cdot r^{n-1}}\\\\\mathrm{a_{13} = -3\cdot (-2)^{13-1}}\\\\\mathrm{a_{13} = -3\cdot (-2)^{12}}\\\\\mathrm{a_{13} = -3\cdot 4096}\\\\\mathrm{a_{13} = -12288}[/tex]