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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

The Hu family goes out for lunch, and the price of the meal is $58. The sales tax on the meal is 7%, and the family also leaves

Alexxx [7]

58 plus tip of .20

so

58 times 0.2 = 11.6 is the tip

now we add tax (Presuming we son't tax the tip)

58 times 0.07 = 4.06 the tax

so its

58 + 11.6 + 4.06 = $73.66 total cost

8 0

3 years ago

Tristan's pen is 2/3 foot long. His pencil is 5/12 foot long. In feet , what is the conbined length of the pen and pencil

frosja888 [35]

The unsimplified answer is 40/12ft long.

8 0

2 years ago

Read 2 more answers

A factory producing cell phones has the following cost and revenue functions: ()=2+75+2,688 C ( x ) = x 2 + 75 x + 2 , 688 and (

prisoha [69]

Answer:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

Step-by-step explanation:

You recently joined a nature club, and last week you went on a trip with the club into the countryside. Write an email to a friend about this. In your email, you should: . describe the place in the countryside you went to with the nature club explain what you learned during the trip to the countryside . invite your friend to join you on the next nature club trip. The pictures above may give you some ideas, and you can also use some ideas of your own. Your email should be between 150 and 200 words long. You will receive up to 8 marks for the content of your email, and up to 8 marks for the language used.

6 0

2 years ago

10 years ago, there were 35 mountain lions and today there are 21. Find the percent of change.

charle [14.2K]

Answer:

40%

Step-by-step explanation:

I I think they were asking about percentage decrease.percentage decrease=to decrease over original price x 100%

4 0

3 years ago

Show by derivation that P=K÷(V_P)​

Show by derivation that P=K÷(V_P)