Estimate of 2,854x9 help me find it and you’ll get ten points

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

3 years ago

Factorise mx+cx+my+cy With steps!!! x=algebra x

avanturin [10]

Step-by-step explanation:

Hey there!

While factorising you remember to make it take common in most of the expression.

Here;

=mx+cx+my+cy

Take common 'x' in "mx+cx" and 'y' in my + cy.

= x(m+c) + y(m+c)

Now, "(m+c)" common again.

= (m+c) (x+y)

Therefore the factorized form of the expression in (m+c)(x+y).

Hope it helps...

6 0

2 years ago

Read 2 more answers

Identify as a direct variation, inverse variation or neither. is the cost of gasoline a direct or inverse variation with respect

r-ruslan [8.4K]

I would say direct because the more gallons of gasoline used, the bigger the cost.

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2 years ago

How far off the ground is the top of the ladder? URGENT PLS HELP

Naddik [55]

The answer is 10.24695. Which is 10.2 for you!

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2 years ago

Suppose you have 34 bread slices and 24 cheese slices. how many cheese sandwiches can you make

Brums [2.3K]

17 if you maintain the ratio of 2:1 for bread and cheese, but you would get a remainder of 7 cheese slices. You could, however, cut up the extra pieces of cheese and add ~0.41 slices of cheese to each sandwich, which would melt into the rest of the cheese if you are grilling the sandwich. Otherwise, it's just an extra chunck, which is perfectly fine.

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3 years ago