1. which of the following is true and radio waves?

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

4 years ago

Madison spent 3 times as long on her social project as she did on her other project. If she spent a total of 8 hours on he proje

deff fn [24]

Answer:

6 hours

Step-by-step explanation:

Suppose Madison spent x hours on her social project,

then the number of hours spent on other project will be 1/3 of x=x/3

Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e

x + x/3 = 4x/3

It si given that this is 8 hours, therefore

4x/3=8

Multiplying both sides by 3:

4x=24

Dividing across board by 4:

x= 6 hours

5 0

3 years ago

Which of these quadrilaterals have opposite sides that are parallel? Name these quadrilateral

Ad libitum [116K]

Answer:

square,rectangle,rhombus,paralellagram

Step-by-step explanation:

4 0

2 years ago

What is the y intercept of the line -4x + 6y = -12?

snow_lady [41]

-4x + 6y = -12
-4(0) + 6y = -12
 0 + 6y = 12
 6y = 12
 6 6
 y = 2

The y-intercept of the equation is 2.

6 0

3 years ago

How large is one side of the square garden plot in meters

Anna [14]

Seeing as area = length X width, we can say that 3 meters X 12 meters = 36… meters. With that statement, it can be assumed that (since the area of the square and rectangle are equal) the area of the square is 36.

7 0

3 years ago