Answer:
The first five terms are [tex]-1,2,8,20,44[/tex].
Step-by-step explanation:
The sequence is defined recursively by the formula [tex]a_n=2\times(a_{n-1})+4[/tex].
The first term of the sequence is given to be, [tex]a_1=-1[/tex].
To find the next term, we substitute [tex]n=2[/tex] in to the above formula to get,
[tex]a_2=2\times(a_{2-1})+4[/tex].
[tex]\Rightarrow a_2=2\times(a_{1})+4[/tex].
But [tex]a_1=-1[/tex]
[tex]\Rightarrow a_2=2(-1)+4[/tex].
[tex]\Rightarrow a_2=-2+4[/tex].
[tex]\Rightarrow a_2=2[/tex].
To find the third term, we substitute [tex]n=3[/tex] in to the above formula to get,
[tex]a_3=2\times(a_{3-1})+4[/tex].
[tex]\Rightarrow a_3=2\times(a_{2})+4[/tex].
But [tex]a_2=2[/tex]
[tex]\Rightarrow a_3=2(2)+4[/tex].
[tex]\Rightarrow a_3=4+4[/tex].
[tex]\Rightarrow a_3=8[/tex].
To find the fourth term, we substitute [tex]n=4[/tex] in to the above formula to get,
[tex]a_4=2\times(a_{4-1})+4[/tex].
[tex]\Rightarrow a_4=2\times(a_{3})+4[/tex].
But [tex]a_3=8[/tex]
[tex]\Rightarrow a_4=2(8)+4[/tex].
[tex]\Rightarrow a_4=16+4[/tex].
[tex]\Rightarrow a_4=20[/tex].
To find the fifth term, we substitute [tex]n=5[/tex] in to the above formula to get,
[tex]a_5=2\times(a_{5-1})+4[/tex].
[tex]\Rightarrow a_5=2\times(a_{4})+4[/tex].
But [tex]a_4=20[/tex]
[tex]\Rightarrow a_5=2(20)+4[/tex].
[tex]\Rightarrow a_5=40+4[/tex].
[tex]\Rightarrow a_5=44[/tex].
Therefore, the first five terms are [tex]-1,2,8,20,44[/tex]. The correct answer is C
