All categories

3 years ago

4th term of an arithmetic sequence is 23 and its 11th term is 65, what is its common difference

Mathematics

1 answer:

Rudik [331]3 years ago

5 0

Answer:

d = 6

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₄ = 23 and a₁₁ = 65 , then

a₁ + 3d = 23 → (1)

a₁ + 10d = 65 → (2)

Subtract (1) from (2) term by term to eliminate a₁

10d - 3d = 65 - 23

7d = 42 ( divide both sides by 7 )

d = 6

You might be interested in

PLSSSSS HELPPPPPP MEH ;^; What is the lateral surface area of the triangular prism?

Zarrin [17]

Answer:

I think it's 56.4

Step-by-step explanation:

if not I'm sorry

8 0

3 years ago

Read 2 more answers

1.The coordinates of the vertices of △RST are R(−4, −1) , S(−1, −1) , and T(−4, −2) .

Leni [432]

1. c, b

2. c, b 1.

To solve this problem, you really need to get a piece of graph paper and draw the triangles. For the triangle RST, you'll see that it's a right triangle with R being the right angle. The long leg of the triangle is close to the origin and the short leg is immediately below R. Then when you draw the triangle R'S'T', you'll see that it's still a right triangle. But now the long leg is parallel to the y axis and S' is now above R' instead of S being to right of R in the original triangle. So it looks like the triangle was rotated 90 degrees counter clockwise which is choice "c". So, draw a new triangle R"S"T" by rotating triangle RST 90 degrees counter clockwise. You'll see that point R" is at (1,-4), S" at (1,-1), and T" at (2,-4). All three of those points are located 2 units below the points R' S' T'. So you need to translate the triangle 2 units higher, which is choice b. 2. This is the exact same question with the exact same choices as #1 above. So the answer is exactly the same.

3 0

4 years ago

Read 2 more answers

What are the domain and range of the function represented by the table?

andrew-mc [135]

Answer:

A. Domain: {-8, -6, -4, -2, 0} Range: {2}

Step-by-step explanation:

The domain of a function is the x values, the range is the y values. you order them in either greatest to least or least to greatest (keep this consistent in both domain and range values). also, if a value repeats, only list it once (this is why the range is {2} rather than {2, 2, 2, 2, 2} )

5 0

3 years ago

Sarah bought an autographed football for $300. The value of the football has increased $50 every year since she purchased the fo

shutvik [7]

Answer:

Step-by-step explanation:

300+50t=v

3 0

3 years ago

Mr. Sánchez owns a square field. The side lengths are 0.9 kilometers. There are 1,980 prairie dog burrows in the fields. What is

Simora [160]

The first thing we are going to do is find the area of the field. To do this we are going to use the area of a square formula: $A=s^2$
Were
$A$ is the area in square kilometers
$s$ is one of the sides of the square
We know for our problem that the side lengths of the field are 0.9 kilometers, so $s=0.9$ . Lets replace that value in our formula to find $A$ :
$A=(0.9)^2$
$A=0.81$

Now, to find the population density of the filed, we are going to use the population density formula: $P_{d}= \frac{I}{A}$
where
$P_{d}$ is the population density in in burrows per square kilometer
 $I$ is the number of burrows
$A$ is the are of the field
We know that $I=1980$ and $A=0.81$ , so lets replace those values in our formula:
$P_{d}= \frac{1980}{0.81}$
$P_{d}=2444.4$

We can conclude that the density of prairie dog burrows is approximately 2444 burrws per square kilometer.

5 0

3 years ago

4th term of an arithmetic sequence is 23 and its 11th term is 65, what is its common difference​

4th term of an arithmetic sequence is 23 and its 11th term is 65, what is its common difference