All categories

2 years ago

Consider the following sequence: -5, -1, 3,...

Mathematics

1 answer:

Alika [10]2 years ago

4 0

Answer:

a. it is arithmentic - this is because for each term there is a constant increase of 4, and the change between each term doesn't change

b. you need to find the nth term, by using the equation difference x n + 0th term: the difference is (+)4 and the 0th term is -9 (-5 is the 1st term, so to go one back we subtract 4 - the inverse operation), so the nth term is 4n -9. Now we do the inverse operation on 119 to see if it's a term (it is a term if it's an integer. So, first we do 119 plus 9 (inverse of - 9) to get 128, then divide it by 4 rather than multiplying. This gives us 32, and that tells us that 119 is the 32nd term of the sequence.

You might be interested in

Identify the initial amount and the growth rate of the following: Y = 9.8 (1.35)^t

stiv31 [10]

Assuming t is a time unit.
The initial amount is when t = 0, so it is 9.8 * 1 = 9.8. The growth rate is how much the amount goes up by for every increase of 1 in t. This is 1.35 because that is the part being affected by t. we plug in 0 for t to get 9.8 as the initial amount. The growth rate is just 135% factor, or 35% more each time, because 1.35 is the base of the exponent.

4 0

2 years ago

5) –2x – 9y=-25 -4x – 9y=-23

notka56 [123]

Answer:

(-1,3)

Step-by-step explanation:

–2x – 9y=-25

-4x – 9y=-23

Multiply the second equation by -1

4x + 9y=23

Add this to the first equation

–2x – 9y=-25

4x + 9y= 23

-----------------------

2x = -2

Divide each side by 2

2x/2 = -2/2

x = -1

Now we need to find y

4x+9y = 23

4(-1) +9y = 23

-4 +9y = 23

Add 4 to each sdie

-4+4 +9y = 23+4

9y = 27

Divide each side by 9

9y/9 = 27/9

y =3

5 0

2 years ago

Read 2 more answers

Find a1, for the arithmetic series with S14 = - 420 and d = -6.

faust18 [17]

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} n = 14\\ d= -6 \end{cases} \\\\\\ a_{14}=a_1+(14-1)(-6)\implies a_{14}=a_1+(13)(-6)\implies a_{14}=a_1-78 \\\\[-0.35em] ~\dotfill$

$\bf \textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ \cline{1-1} n= 14\\ S_{14}=-420\\ a_{14}=a_1-78 \end{cases}\implies S_{14}=\cfrac{n(a_1+a_{14})}{2} \\\\\\ -420=\cfrac{14[a_1+(a_1-78)]}{2}\implies -420=7(2a_1-78)\implies \cfrac{-420}{7}=2a_1-78 \\\\\\ -60=2a_1-78\implies 18=2a_1\implies \cfrac{18}{2}=a_1\implies 9=a_1$

8 0

3 years ago

Can someone help me please

vovikov84 [41]

X=7

Explanation:

A triangle equals 180°, and they gave us one length already, and it says the one arm of the triangle is equal to the other so we know that the third angle is going to be the same as the second angle.

180=90+(6x+3)+(6x+3)
Combine like terms
180=96+12x
Subtract 96 from both sides
84=12x
Divide 12 by both sides
7=x

Now check it,

90+(6*7+3)+(6*7+3)
90+(45)+(45) =180

8 0

2 years ago

Find the solution set. |x| = -16 { } {-4, 4} {-16, 16} {-32, 32}

Otrada [13]

This an { } solution because the absolute value is always a positive number unless there is a negative sign in front of the brackets.

hope this helps :)

7 0

2 years ago

Read 2 more answers