QUESTION 1
The given sequence is [tex]3,-9,27,-81,...[/tex].
The first term of the sequence is [tex]a_1=3[/tex]
The second term is [tex]a_2=-9[/tex]
The common ratio can be found using any two consecutive terms of the sequence.
Thus, the common ratio is given by [tex]r=\frac{a_n}{a_{n-1}}[/tex].
This implies that,
[tex]r=\frac{-9}{3}[/tex]
This simplifies to,
[tex]r=-3[/tex]
The correct answer is C
QUESTION 2
The sum of the first n terms of a geometric sequence is given by;
[tex]S_n=\frac{a_1(r^n-1)}{r-1}[/tex].
Since we are looking for the first five terms, we substitute [tex]n=5[/tex], [tex]a_1=3[/tex] and [tex]r=-3[/tex] into the formula to obtain,
[tex]S_5=\frac{3((-3)^5-1)}{-3-1}[/tex]
This will evaluate to give us;
[tex]S_5=\frac{3(-243-1)}{-3-1}[/tex]
[tex]S_5=\frac{3(-244)}{-4}[/tex]
[tex]\Rightarrow S_5=3\times 61[/tex]
[tex]\Rightarrow S_5=183[/tex]
The correct answer is A
