Answer: The fourth term is -102
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Explanation:
The term after the nth term is generated by this rule [tex]a_{n+1} = -4(a_n) + 2[/tex] which means that we first
Step 1) multiply the nth term ( [tex]a_n[/tex] ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence
Let's follow those steps above to generate the first four terms
The first term is [tex]a_1 = 2[/tex]. In short, the first term is 2
The second term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{1+1} = -4(a_1) + 2[/tex]
[tex]a_{2} = -4(2) + 2[/tex]
[tex]a_{2} = -8 + 2[/tex]
[tex]a_{2} = -6[/tex]
So the second term is -6
The third term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{2+1} = -4(a_2) + 2[/tex]
[tex]a_{3} = -4(-6) + 2[/tex]
[tex]a_{3} = 24 + 2[/tex]
[tex]a_{3} = 26[/tex]
The third term is 26
Finally, the fourth term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{3+1} = -4(a_3) + 2[/tex]
[tex]a_{4} = -4(26) + 2[/tex]
[tex]a_{4} = -104 + 2[/tex]
[tex]a_{4} = -102[/tex]
The fourth term is -102.
