Ok don't hurt yourself I'm here ...
[tex]a(n) = 3a(n - 1) + 5[/tex]
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n = 2
put 2 instead of any "n" you can see in the above equation
[tex]a(2) = 3a(2 - 1) + 5[/tex]
[tex]a(2) = 3a(1) + 5[/tex]
Oh can you see that " a(1) " we know what it is :
[tex]a(1) = - 3[/tex]
So :
[tex]a(2) = 3 \times ( - 3) + 5[/tex]
[tex]a(2) = - 9 + 5[/tex]
[tex]a(2) = - 4[/tex]
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n = 3
put 3 instead of blablabla...
[tex]a(3) = 3a(3 - 1) + 5[/tex]
[tex]a(3) = 3a(2) + 5[/tex]
Oh we just found a(2) so :
[tex]a(3) = 3( - 4) + 5[/tex]
[tex]a(3) = - 12 + 5[/tex]
[tex]a(3) = - 7[/tex]
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n = 4
put 4 ...
[tex]a(4) = 3a(4 - 1) + 5[/tex]
[tex]a(4) = 3a(3) + 5[/tex]huh a(3)
[tex]a(4) = 3( - 7) + 5[/tex]
[tex]a(4) = - 21 + 5[/tex]
[tex]a(4) = - 16[/tex]
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So the first four term of the sequence is :
[tex] - 3 \: , \: - 4 \: , \: - 7 \: , \: - 16[/tex]
There u go...
Have a great day ♡
