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Contact [7]
3 years ago
8

the first four terms of an arithmetic sequence are 2,a-b, 2a+b+7 and a - 3b, where a and b are constants. Find a and b

Mathematics
1 answer:
SashulF [63]3 years ago
7 0

Arithmetic Sequence

The  values of a and b is a = 2 and b=3

Step-by-step explanation:

Given the terms of the arithmetic sequence are

2 , a - b ,  2a + b + 7, a - 3b

Let the common difference be D

Therefore,

The difference between the first two consecutive terms is

(a – b) – 2 = D        ------------------------------( 1 )

The difference between the next two consecutive terms is

D = (2a + b+7) – ( a - b ) ---------------------(2 )

Equating equation 1 and equation 2

⇒ (a – b) -2 =(2a+b+7)-(a-b)

⇒ a – b – 2 =  a + 2b +7

⇒ 3b = -9

⇒ b = -3

Similarly

The difference between the next two consecutive terms is

D = (a-3b)-(2a+b+7) -------  (3)

⇒ (a-3b)-(2a+b+7)=(2a+b+7)-(a-b)    

⇒ a-3b)-(2a+b+7) -a  - 4b -7 === a+2b+7

⇒ 2a = - ( 14 + 6b)

⇒  a = -( 7 + 3b)

⇒  a = - ( 7 – 3*3 )

Thus the value of a = 2

Hence , the values of a and b is a = 2 and b=3

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Answer:

1) +80

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Step-by-step explanation:

Positive Signed numbers are used in real world situations to indicate the increase. Examples include; increase in weight, deposit of money into an account, increase in income, profit, height above sea level, etc. They are all represented by positive signed numbers.

Whereas, negative signed numbers show decrease. Examples include; loss of weight, withdrawal of money from an account, loans, liabilities, losses, temperature below zero degrees, height below sea level.

1) We are told that Reuben received 80 dollars. Thus, it means he received an increase in the amount of money he already had. Thus, the signed number will be +80.

2) We are told that A car corporation produced 1520 fewer cars this month than last.

Thus, the signed number will be negative since there is a decrease in number of cars.

Thus, signed number = -1520

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2 years ago
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
guajiro [1.7K]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
Can someone help me i cant understand with work
Masja [62]

Answer:

Right now it would be

-40

Since desend means down add -20 to -40

-40+(-20)=-60

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-40-20=-60

Then is goes up 35, which is positive

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Therefore, the answer is -25

Hope this helps

Answer by

<em>Fishylikeswater</em>

<em></em>

3 0
3 years ago
Read 2 more answers
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ehidna [41]
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The final answer is 5(x+2+3y)~
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