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3 years ago

Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .? n

Mathematics

1 answer:

zalisa [80]3 years ago

3 0

Answer:

Step-by-step explanation:

In the given sequence, the terms are increasing in arithmetic progression. The common difference, d between successive terms is 2

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 1

d = 2

Therefore, the expression for the general term for the sequence is

Tn = 1 + 2(n - 1)

You might be interested in

A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago

A boy purchased (bought) a party-length sandwich 51 in. long. He wants to cut it into three pieces so that the middle piece is

shepuryov [24]

Answer:

Step-by-step explanation:

we have a 51 in sandwich

let a piece be x

we have x= shorter piece

another piece is x+6

another piece (x+6)-9=x-3

x+x+6+x-3=51

3x=51-3

3x=48

x=48/3=16

x=16, longer piece is 16+6=22, shorter piece =10

6 0

2 years ago

Evaluate AB for A = 5, B =-2, C = 4 and D = -6.<br> 5/12<br> -5/12<br> -3/2<br> 3/2

Nezavi [6.7K]

Answer:

AB = -10

Im confused is this what you wanted?

5 0

3 years ago

I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some

sergiy2304 [10]

1. +
2.divide
3. *
4. Divide
5. -
6. +
7. -
8.*
9. 2 and 5

8 0

3 years ago

E and F are complementary. If m E = 9x - 38 and mF = 2x + 40, find m F pls I need help

larisa86 [58]

Answer:

<h2>m $\angle$ F = 34°</h2>

Step-by-step explanation:

If E and F are complementary I means that the sum of their angles add up to 90° since all complementary angles have the sum of their angles equal to 90°

To find m $\angle$ F add m $\angle$ E and m $\angle$ F and equate it to 90 to find x then substitute it into the expression for m $\angle$ F

Thats

m $\angle$ E + m $\angle$ F = 90

$\rarr$ 9x - 38 + 2x + 40 = 90

$\rarr$ 11x + 2 = 90

$\rarr$ 11x = 90 - 2

$\rarr$ 11x = 88

Divide both sides by 11

x = 8

Now we have

if m $\angle$ F = 9x - 38

m $\angle$ F = 9( 8) - 38

m $\angle$ F = 72 - 38

We have the final answer as

<h3>m $\angle$ F = 34°</h3>

Hope this helps you

4 0

3 years ago