MATH SOLVE

2 months ago

Q:
# Consider the following sequence of numbers 3, -9, 27, -81, β¦. Common Ratio Of The Sequence is? A. 1/3B. -1/3C. -3D. 3The Sum Of The First Five Terms Of The Sequence Is? A. 183B. -303C. -60D. 363

Accepted Solution

A:

QUESTION 1The 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 2The 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

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 2The 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