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Sagot :
Answer: 7, 15, 39, 111, 327
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Work Shown:
First replace every copy of n with 2
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_2 = 3*(a_{2-1}) - 6\\\\a_2 = 3*(a_{1}) - 6\\\\a_2 = 3*(7) - 6\\\\a_2 = 21 - 6\\\\a_2 = 15\\\\[/tex]
Notice how the second term [tex]a_2[/tex] relies on the first term [tex]a_1[/tex]
Then repeat for n = 3
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_3 = 3*(a_{3-1}) - 6\\\\a_3 = 3*(a_{2}) - 6\\\\a_3 = 3*(15) - 6\\\\a_3 = 45 - 6\\\\a_3 = 39\\\\[/tex]
Same goes with n = 4
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_4 = 3*(a_{4-1}) - 6\\\\a_4 = 3*(a_{3}) - 6\\\\a_4 = 3*(39) - 6\\\\a_4 = 117 - 6\\\\a_4 = 111\\\\[/tex]
Finally plug in n = 5
[tex]a_n = 3*(a_{n-1}) - 6\\\\a_5 = 3*(a_{5-1}) - 6\\\\a_5 = 3*(a_{4}) - 6\\\\a_5 = 3*(111) - 6\\\\a_5 = 333 - 6\\\\a_5 = 327\\\\[/tex]
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We have this summary:
[tex]a_1 = 7\\\\a_2 = 15\\\\a_3 = 39\\\\a_4 = 111\\\\a_5 = 327\\\\[/tex]
The first five terms are: 7, 15, 39, 111, 327
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