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wolverine [178]
3 years ago
14

Consider the arithmetic sequence 13, 24, 35, ....

Mathematics
1 answer:
MArishka [77]3 years ago
8 0

Answer:

The explicit form for the sequence is: a_{n}=13+(n-1)(11)

Step-by-step explanation:

In order to find an explicit form for the given sequence, you have to use the definition of arithmetic sequence and the <em>explicit formula</em>.

An arithmetic sequence is defined as a sequence where the difference of two consecutive terms is a constant.

The <em>explicit formula </em>is:

a_{n}=a_{1} + (n-1)d

Where a1 is the first term, d is the common difference and an is the nth term of the sequence.

You have to subtract two consecutive terms to obtain d:

24-13= 11

35-24=11

Therefore d=11

In this case a1=13

Replacing in the formula:

a_{n}=13+(n-1)(11)

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(2*2)^2-(3+(2*2)/(6-4) EXPLAINED PLEASE
Eva8 [605]

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The solution of the given expression (2×2)² - [3+(2×2)]/(6-4) is 14.

<h3>What is PEMDAS?</h3>

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

As per the rule of PEMDAS, the given expression can be simplified as shown below.

(2×2)² - [3+(2×2)]/(6-4)

Step 1: Solving Parenthesis,

= 4² - (3+4) / (2)

= 4² - 4/2

Step 2: Solving exponents,

= 16 - 4/2

Step 3: Solving Divisions,

= 16 - 2

Step 4: Solving Subtraction,

= 14

Hence, the solution of the given expression (2×2)² - [3+(2×2)]/(6-4) is 14.

Learn more about PEMDAS here:

brainly.com/question/36185

#SPJ1

6 0
1 year ago
2. You bought items at Best Buy totaling $290.76. You have a 20%
vovangra [49]

Answer:

Discount = $290.76 × 0.2 = $58.15

Cost After Discount = $290.76 - $58.15 = $232.61

Sales Tax = 0.0625 × $232.61 = $14.56

How Much You Pay = $232.61 + $14.56 = $247.17

Step-by-step explanation:

Discount:

290.76 × 0.2* = 58.152

Round that to 58.15

* Turn 20% into a decimal (0.2)

Cost after Discount:

290.76 - 58.15 = 232.61

Sales Tax:

First turn 6.25 % into a decimal. Which would be 0.0625.

0.0625 × 232.61* = 14.556875

Then we round to the nearest hundredth and you get 14.56.

* We us the amount after the discount instead of the original price.

How much you pay:

232.61 + 14.56 = 247.17

8 0
3 years ago
A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hos
Lady_Fox [76]

Null hypothesis: p = 0.81

Alternative hypothesis: p \ne 0.81

The null is based on a recent study that 81% of the population (in this case senior citizens) takes at least one medication. The alternative hypothesis is basically the flip of the claim made in the null.

If Amelia wanted to know if the percentage was less than 81%, then the alternative would be p < 0.81

If Amelia wanted to know if the percentage was larger than 81%, then the alternative would be p > 0.81

However, she wants to know if the percentage is 81%.

5 0
2 years ago
F(1) = 4<br> f(x) = f(x-1) + 3<br> Find f(2)
tester [92]

f(2)= f(2-1)+3

f(2)=f(1)+3

4 0
2 years ago
A rectangular deck is 12ft by 14ft. When the length and width are increased by the same amount, the area becomes 288sq. ft. By h
Cerrena [4.2K]

Dimensions of rectangle = 12 + x and 14 + x

(12 + x) (14 + x) = 288

 x^2 + 26x + 168 = 288

 x^2 + 26x - 120 = 0


(x + 30) (x - 4) = 0

x=-30, x =4

 since 4 is positive

 the dimensions increased by 4 feet

check the answer

12+4 = 16

14 +4 = 18

18*16 =288

 


3 0
3 years ago
Read 2 more answers
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