Question

A student is attempting to find a formula for the sequence below. Which statement best applies to the sample mathematical work?

Given the sequence 3, –9, 27, ..., I first find the ratio of the terms. I find that the ratio is -9/3=-3 So I plug this value into the formula to get ^a n=(-3)^n-1 as a final answer.
A.
The ratio is calculated improperly.
B.
The formula does not take into account the first term of the sequence.
C.
The sequence is not a geometric sequence, so the equation used is wrong.
D.
The sample mathematical work is correct.

Answer 1

Answer : B

Explanation:

Our sequence is 3,-9,27,........This is a geometric sequence. whose first terms is 3 which is generally denoted by "a" .The common ratio is find out by taking the ration of second term to the first term. In this case it would be ,

`r=(-9)/(3)`

Hence r=-3

Now the formula for the nth term of any geometric sequence is given as

`a_(n)` =
`ar^(n-1)`

Hence we now replace the value of a and r in this to find the right answer which is

`a_(n) = 3(-3)^(n-1)`

Hence B option is correct as the first term is not taken into the account in this answer.

Answer 2

the sample is a geometri sequencethe ratio = -9 / 3 = -3= 27 / -9 = -3so it is clearly a geometric sequencethen the formula of a geometric sequence:
an = ar^(n-1)where an is the n terma is the initial termr is the rationn is the number of term
an = 3(-3)^(n-1)is the answer