Question

Consider the following sequence of numbers 3, -9, 27, -81, ….

Answer 1

QUESTION 1

The given sequence is $3,-9,27,-81,...$.

The first term of the sequence is $a_1=3$

The second term is $a_2=-9$

The common ratio can be found using any two consecutive terms of the sequence.

Thus, the common ratio is given by $r=\frac{a_n}{a_{n-1}}$.

This implies that,

$r=\frac{-9}{3}$

This simplifies to,

$r=-3$

The correct answer is C

QUESTION 2

The sum of the first n terms of a geometric sequence is given by;

$S_n=\frac{a_1(r^n-1)}{r-1}$.

Since we are looking for the first five terms, we substitute $n=5$, $a_1=3$ and $r=-3$ into the formula to obtain,

$S_5=\frac{3((-3)^5-1)}{-3-1}$

This will evaluate to give us;

$S_5=\frac{3(-243-1)}{-3-1}$

$S_5=\frac{3(-244)}{-4}$

$\Rightarrow S_5=3\times 61$

$\Rightarrow S_5=183$

The correct answer is A

Answer 2

Answer:

Q1.  A ; 1/3

Hope this helps !