Answer: 234
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Explanation:
As you can probably guess, the first equation [tex]a_1 = 3[/tex] says that the first term is 3. The small '1' indicates "first term". So writing [tex]a_2[/tex] represents the second term, then [tex]a_3[/tex] is notation for the third term, and so on.
The second term is found by plugging in n = 2 into the second equation and computing to get...
[tex]a_n = 4*a_{n-1} + 2\\\\a_2 = 4*a_{2-1} + 2\\\\a_2 = 4*a_{1} + 2\\\\a_2 = 4*3 + 2\\\\a_2 = 12 + 2\\\\a_2 = 14\\\\[/tex]
The second term is 14. The steps above basically say: "to get the second term, we multiply the first term by 4, then add on 2"
In other words,
second term = 4*(first term) + 2
second term = 4*(3) + 2
second term = 12 + 2
second term = 14
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This can be extended to get the third term
third term = 4*(second term) + 2
third term = 4*(14) + 2
third term = 56 + 2
third term = 58
and finally,
fourth term = 4*(third term) + 2
fourth term = 4*(58) + 2
fourth term = 232 + 2
fourth term = 234
