Mathematics, 30.07.2019 19:00 invocx

Part 1.] indicate the general rule for the arithmetic sequence with $a_{3}=-4$ and $a_{8}=-29$ a.] $a_{n}=-6+(n-)$ b.] $a_{n}=-6+(n-1)(5)$ c.] $a_{n}=6+(n-)$ d.] $a_{n}=6+(n-1)(5)$ part 2.] which of the following is the general term for the sequence m, -m, m, -m, . .? a.] $m(-1)^{n-1}$ b.] $(-m)^{n}$ c.] $(-1)m^{n+1}$ d.] $(-1)m^{n-1}$ part 3.] indicate a general rule for the $n^{th}$ term of the sequence when $a_{1}=5$ and $r= \sqrt{3}$ a.] $a_{n}=( \sqrt{3})(5)^{n+1}$ b.] $a_{n}=( \sqrt{3})(5)^{n-1}$ c.] $a_{n}=(5)( \sqrt{3})^{n-1}$ d.] $a_{n}=(5)( \sqrt{3})^{n+1}$

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These are 3 questions and 3 answers.

Part 1.] Indicate the general rule for the arithmetic sequence with A3 = - 4 and A8 = - 29

option C. An = 6 + (n-1)(-5)

Solution:

1) A3 is the third term
2) A8 is the eigth term
3) The formula for arithmetic sequences is: An = Ao + (n - 1)d

where n is the number of term and d is the difference between two consecutive terms.

=>

4) A8 = Ao + (8 - 1)d = - 29 => Ao + 7d = - 29 [equation 1]

5) A3 = Ao + (3 - 1)d = - 4 => Ao + 2d = - 4 [equation 2]

6) Subtract equation 2 from equation 1 => 7d - 2d = - 29 - (-4) =>

5d = - 29 + 4
5d = - 25
d = - 25/5 = - 5

7) Find Ao using equation 2:

Ao + 2d = - 4 =>
Ao = - 4 - 2d = - 4 - 2(- 5) = - 4 + 10 = 6

8) General rule: An = 6 + (n - 1) (-5) < option C.

Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?

option a. m (-1)^ (n-1).

Justification:

the sign of the coefficient changes for each term.

when n = 1, the sign is positive: (-1)^ (1-1) = 1
when n = 2, the sign is negative: (-1)^ (2-1) = - 1
when n = 3, the sign is positive: (-1)^ (3-1) = 2

And so on. So, m (-1)^ (n-1) does the work.

Part 3.] Indicate a general rule for the nth term of the sequence when A1 = 5 and r = √3

option C. An = (5)(√3)^(n-1)

Explanation:

This is a geometric sequence with A1 = 5 and r = √3

The terms of the geometric sequence are:

A1 = 5
A2 = A1 * √3 = 5√3
A3 = A2 * √3 = 5(√3)(√3) = 5(3) = 15
A4 = A3 * √3 = 15√3

So, the general expression is An = 5 * (√3)^(n-1), which is the option C.

Answer from: Quest

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Answer from: Quest

answer:

step-by-step explanation:

odd numbers are only divisible by 1 and itself.

even numbers are divisible by more than 1 and itself.

for example 6 is even because it is divisible by more than 1 and its self. 1 x 6= 6 ; 2 x 3= 6

and 7 is odd because only 7 x 1 equals seveb

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Part 1.] indicate the general rule for the arithmetic sequence with [tex] a_{3}=-4[/tex] and [tex] a...

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