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Tomtit [17]
2 years ago
14

Solve the equation. Check your solution.

Mathematics
1 answer:
zzz [600]2 years ago
3 0
I’m pretty sure it’s -4
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Write a recursive formula and an explicit formula for the following arithmetic sequence.
xenn [34]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

so

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

  • aₙ₊₁ = aₙ+2, for n ≥1

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2

The difference between all the adjacent terms is the same and equal to

d=2

also

a_1=11

so substituting d=2, a_1=11 in the nth terms

a_n=a_1+\left(n-1\right)d

a_n=2\left(n-1\right)+11

a_n=2n+9

Therefore, the Explicit formula is:

a_n=2n+9

4 0
2 years ago
Lucy’s parents built a swimming pool in the backyard. Use 3.14 for π.
Rus_ich [418]

Answer:

Distance around the pool = 162.8 feet

Area of the pool = 957 square feet

Step-by-step explanation:

Distance around the swimming pool = Perimeter of the pool

Perimeter of the pool which is a composite figure will be,

= Circumference of the semicircle + Sum of three sides of the pool

= πr + 2×(length of the pool) + width of the pool

= 3.14×(10) + 2×40 + 20

= 62.8 + 80 + 20

= 162.8 ft

Area of the pool = Area of the semicircle + Area of the rectangular pool

                           = \frac{1}{2}(\pi)(r)^{2}+(\text{length}\times \text{Width})

                           = \frac{1}{2}(3.14)(10)^2+(40\times 20)

                           = 157 + 800

                           = 957 square feet

8 0
3 years ago
Are two equilateral triangles always equal
weqwewe [10]
No not always the degrees maybe
 i hope this helps
6 0
2 years ago
Read 2 more answers
How many sets of four consecutive positive integers are there such that the product of the four integers is less than $100,\!000
SVEN [57.7K]

Answer:

16,17,18,19

Step-by-step explanation:

one guy guessed. probably using a calculator

another guy took the 4th root of 100,000 and rounded down a number

(a third way started like this

n*(n+1)*(n+2)(n+3)=100000

4 0
2 years ago
Four added to 3 times a number is 25
lukranit [14]

The answer is 13. To solve this you have to do 4*3 which is 12. Then you subtract 25 and 12 to get an answer of 13.

4 0
3 years ago
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