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hammer [34]
3 years ago
15

Last questions, plz help

Mathematics
1 answer:
Goryan [66]3 years ago
5 0

Answer:

9. a_n=7+6n

10. a_n=a_{n-1}+7

Step-by-step explanation:

9. Given the sequence

13, 19, 25, ...

In this sequence,

a_1=13\\ \\a_2=19\\ \\a_3=25\\ \\...

Note that

a_2-a_1=19-13=6\\ \\a_3-a_2=25-19=6,

then the common difference in this sequence is d=6

You have

a_1=13\\ \\d=6,

then the explicit formula is

a_n=a_1+(n-1)d\\ \\a_n=13+(n-1)\cdot 6\\ \\a_n=13+6n-6\\ \\a_n=7+6n

10. Given the sequence

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

In this sequence,

a_1=-10\\ \\a_2=-3\\ \\a_3=4\\ \\a_4=11\\ \\...

Note that

a_2-a_1=-10-(-3)=-10+3=-7\\ \\a_3-a_2=-3-4=-7\\ \\a_4-a_3=11-4=7,

then the common difference in this sequence is d=7

You have

a_1=-10\\ \\d=7,

then the recursive formula is

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

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Could someone please help me with this? I would mark you as Brainliest:)
Hunter-Best [27]

Answer:

a) The table of values represents the ordered pairs formed by the elements of the sequence (a_{i}) (range) and their respective indexes (i) (domain):

i         a_{i}

1         6

2        11

3        16

4        21

5        26

b) The algebraic expression for the general term of the sequence is a(i) = 6 + 5\cdot (i - 1).

c) The 25th term in the sequence is 126.

Step-by-step explanation:

a) Make a table of values for the sequence 6, 11, 16, 21, 26, ...

The table of values represents the ordered pairs formed by the elements of the sequence (a_{i}) (range) and their respective indexes (i) (domain):

i         a_{i}

1         6

2        11

3        16

4        21

5        26

b) Based on the table of values, we notice a constant difference between two consecutive elements of the sequence, a characteristic of arithmetic series, whose form is:

a(i) = a_{1} + r\cdot (i - 1) (1)

Where:

a_{1} - First element of the sequence.

r - Arithmetic difference.

i - Index.

If we know that a_{1} = 6 and r = 5, then the algebraic expression for the general term of the sequence is:

a(i) = 6 + 5\cdot (i - 1)

c) If we know that a(i) = 6 + 5\cdot (i - 1) and i = 25, then the 25th term in the sequence is:

a(25) = 6 + 5\cdot (25 - 1)

a(25) = 126

The 25th term in the sequence is 126.

7 0
2 years ago
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 550-meter head st
andrew-mc [135]

Answer:

a) distance covered by hare d1 = 8t

b) distance covered by tortoise d2 = 5t + 550

c) ∆d = 550 - 3t

Step-by-step explanation:

Given;

Speed of hare u = 8m/s

Speed of tortoise v = 5 m/s

Initial distance of tortoise d0 = 550 m

a) using the equation of motion;

distance covered = speed × time + initial distance

d = vt + d0

For hare;

d0 = 0

Substituting the values;

d1 = 8t + 0

d1 = 8t

b)using the equation of motion;

distance covered = speed × time + initial distance

d2 = vt + d0

For tortoise;

d0 = 550m

Substituting the values;

d2 = 5t + 550

d2 = 5t + 550 m

c) the number of meters the tortoise is ahead of the hare.

∆d = distance covered by tortoise - distance covered by hare

∆d = d2 - d1

Substituting the values;

∆d = (5t + 550) - 8t

∆d = 550 - 3t

6 0
3 years ago
Llana ran 2 laps around the field in 8 minutes. what was he average speed
son4ous [18]

Answer: 1 Lap Per Every 4 Minutes Is Her Average Speed.

Step-by-step explanation: To find her average speed, simply divide 8 by 2 which is 4.

8/2 = 4 minutes per lap.

3 0
3 years ago
The 9’s in 9,905,482
Sergeu [11.5K]

Answer:Your question is very detailed but I’ll try anyways, there are two 9,s in that number and 9 million is one of them and the other is 900,000

Step-by-step explanation:

If this is wrong you can report it to remove I’m sure,

7 0
2 years ago
The formula for converting a temperature from degrees Fahrenheit to degrees Celsius is C = (F - 32). What is 86°F in °C?
Vadim26 [7]

Answer:

A

Step-by-step explanation:

(86°F − 32) × 5/9 = 30°C

7 0
3 years ago
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