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3 years ago

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?

1 answer:

4 0

So, from the first term, to the fifteen term, there are 14 terms to go through.

that means, if say the common difference is say "d", we have to add "d" 14 times, to get to the 15th term, lemme make a quick table,

$\bf \begin{array}{llll}
term&value\\
----&------\\
1&-3\\
2&-3+d\\
3&-3+d+d\\
4&-3+d+d+d\\
5&-3+d+d+d+d\\
6&-3+d+d+d+d+d\\
7&-3+d+d+d+d+d+d\\
8&-3+d+d+d+d+d+d+d\\
9&-3+d+d+d+d+d+d+d+d\\
10&-3+d+d+d+d+d+d+d+d+d\\
11&-3+d+d+d+d+d+d+d+d+d+d\\
12&-3+d+d+d+d+d+d+d+d+d+d+d\\
13&-3+d+d+d+d+d+d+d+d+d+d+d+d\\
14&-3+d+d+d+d+d+d+d+d+d+d+d+d+d\\
15&-3+d+d+d+d+d+d+d+d+d+d+d+d+d+d\\
&53
\end{array}\\\\
-------------------------------\\\\
-3+14d=53\implies 14d=56\implies d=\cfrac{56}{14}$

and surely you know how much that is.

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. N an 1 4 2 −12 3 36 t

Rzqust [24]

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

<h3>What is sequence ?</h3>

Sequence is collection of numbers with some pattern .

Given sequence

$a_{1}=5\\\\a_{2}=-10\\\\\\a_{3}=20$

We can see that

$\frac{a_1}{a_2}=\frac{-10}{5}=-2\\$

and

$\frac{a_2}{a_3}=\frac{20}{-10}=-2\\$

Hence we can say that given sequence is Geometric progression whose first term is 5 and common ratio is -2

Now $n^{th}$ term of this Geometric progression can be written as

$T_{n}= 5\times(-2)^{n-1}$

So summation of 15 terms can be written as

$\sum_{n=4}^{15} T_{n}\\\\$\\$\sum_{n=4}^{15} 5(-2)^{n-1}$$$

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

To learn more about Geometric progression visit : brainly.com/question/14320920

8 0

3 years ago

These plots show the number of kilometers a group of students at Middleton Middle School and at Westwood Middle School travel to

vitfil [10]

Answer:

<u>Middleton only</u>

Step-by-step explanation:

Sometimes, in a data set, there is a number that is much larger or much smaller than the others generally tend to be. These numbers that are far away from the average are known as outliers

The data set for the students at Middleton Middle School:

1 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 6 9

We can note that most of data is between 1 and 6, the gap between them is 0 or 1, but there is one of the data which is 9, the gap between 9 and 6 is 3

<u>So, 9 would be considered an outlier.</u>

<u>So, The shapes of plots shows an outlier is Middleton only</u>

The data set for the students at Westwood Middle School:

2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6

We can note that all of data is between 2 and 6, the gap between them is 0 or 1

<u>So, There is no outlier for the set of data.</u>

4 0

4 years ago

Read 2 more answers

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ira [324]

Answer:

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Step-by-step explanation:

7 0

3 years ago

(2+6 +8+54 +...);S 12

Aleks [24]

What is the equation?

7 0

3 years ago

Given the piecewise function shown below select all of the statements that are true please help

KengaRu [80]

Answer:

B and D

Step-by-step explanation:

Take a look at all the options x=4, 3, 1, 2 > 0

So, we just care about the domain where x>0, which is $f(x)=x^{2}$ .

Then plug in x we will have the right answer.

5 0

4 years ago