Answer:
-3, -7, -23, -87, and -343
Step-by-step explanation:
Here, we're given that the sequence is [tex]a_n=4a_{n-1}+5[/tex], where n indicates the nth term and n - 1 indicates the (n - 1)th term.
[tex]a_1=-3[/tex], so if we want to find [tex]a_2[/tex], we can say n = 2 and n - 1 = 1:
[tex]a_2=4a_{1}+5=4*(-3)+5=-12+5=-7[/tex]
We continue to do this to find [tex]a_3,a_4,[/tex] and [tex]a_5[/tex]:
[tex]a_3=4a_{2}+5=4*(-7)+5=-28+5=-23[/tex]
[tex]a_4=4a_{3}+5=4*(-23)+5=-92+5=-87[/tex]
[tex]a_5=4a_{4}+5=4*(-87)+5=-348+5=-343[/tex]
Thus, the first 5 terms in the sequence are:
-3, -7, -23, -87, and -343
Hope this helps!
