All categories

3 years ago

Write the rule of the nth term of each sequence 7,4,1,-2

Mathematics

1 answer:

Zarrin [17]3 years ago

8 0

Answer:

$a_{n}$ = 10 - 3n

Step-by-step explanation:

the terms 7, 4, 1, - 2 form an arithmetic sequence with n th term

$a_{n}$ = $a_{1}$ + (n - 1)d

where d is the common difference and $a_{1}$ the first term

here d = - 2 - 1 = 1 - 4 = 4 - 7 = - 3 and $a_{1}$ = 7, hence

$a_{n}$ = 7 - 3(n - 1) = 7 - 3n + 3 = 10 - 3n

You might be interested in

Carlos and Maria drove a total of 217 miles in 4.1 hours. Carlos drove the first part of the trip and averaged 52 miles per hour

VMariaS [17]

M = hours driven by Maria

c = hours driven by Carlos

since we know that Carlos was driving at an average of 52 mph, then in 1 hour he drove 52 miles, in 2 hours he drove 2*52 miles in "c" hours he drove c*52 miles or 52c.

Maria on the other hand is faster and does 54 mph, in 1 hour she does 1 * 54 miles, and on 2 hours she does 2 * 54 miles and in "m" hours she does m * 54 miles or 54m.

now, we know the total amount of miles they both drove is 217, so whatever "m" and "c" are we know that 54m + 52c = 217.

we also know it took 4.1 for the whole trip, so m + c = 4.1.

$\bf \begin{cases}
m+c=4.1\implies \boxed{c}=4.1-m\\
54m+52c=217\\
-------------\\
54m+52\left( \boxed{4.1-m} \right)=217
\end{cases}
\\\\\\
54m-52m+213.2=217\implies 2m=3.8
\\\\\\
m=\cfrac{3.8}{2}\implies m=1.9$

so Maria drove for 1.9 hours.

How many hours did Carlos drive for? well, c = 4.1 - m.

4 0

2 years ago

the strength of students in a school when increased by 8% becomes 2160. find the original strength of students in the school.

Leni [432]

Answer:

1987.2

Step-by-step explanation:

We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other. Since we know the strength of students increased by 8% to 2160 then the original was 92%.

$\frac{92}{100}=\frac{y}{2160}$

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

92(2160)=100(y)

198720=100y

y=1987.2

There are 1987.2 as the original strength of students.

6 0

2 years ago

Which of the following represents the additive inverse of <img src="https://tex.z-dn.net/?f=2%2F3" id="TexFormula1" title="2/3"

PolarNik [594]

C)-2/3is the answer because when your have 2/3+-2/3 will equal 0 in which justifies the additive inverse

7 0

2 years ago

Read 2 more answers

90 units needed 8units per case

lisov135 [29]

Answer: 90/8=11.25

Step-by-step explanation:

8 0

3 years ago

The profit function p(x) of a tour operator is modeled by p(x) = −2x^2 + 700x − 10000, where x is the average number of tours he

pav-90 [236]

Answer:

Range of the average number of tours is between 150 and 200 including 150 and 200.

Step-by-step explanation:

Given:

The profit function is modeled as:

$p(x)=-2x^2+700x-10000$

The profit is at least $50,000.

So, as per question:

$p(x)\geq50000\\-2x^2 + 700x-10000\geq 50000\\-2x^2+700x-10000-50000\geq 0\\-2x^2+700x-60000\geq 0\\\\\textrm{Dividing by 2 on both sides, we get}\\\\-x^2+350x-30000\geq 0$

Now, rewriting the above inequality in terms of its factors, we get:

$-1(x-150)(x-200)\geq 0\\(x-150)(x-200)\leq 0$

Now,

$x0\\x>200,(x-150)(x-200)>0\\For\ 150\leq x\leq200,(x-150)(x-200)\leq 0\\\therefore x=[150,200]$

Therefore, the range of the average number of tours he must arrange per day to earn a monthly profit of at least $50,000 is between 150 and 200 including 150 and 200.

7 0

2 years ago