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Liono4ka [1.6K]
3 years ago
13

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:
jonny [76]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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serious [3.7K]

Answer:

1. >; 2. >  

Step-by-step explanation:

1.

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0.375 (?) 0.295

We can use a <em>number line</em> to decide which number is greater.

In Fig. 1 below, when we go from 0.295 to 0.375, we are moving to the <em>RIGHT</em>,  so 0.375 is greater than 0.295.

0.375 >  0.295

2.

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In Fig. 2 below, when we go from -0.80 to -0.77, we are moving to the <em>RIGHT</em>,  so -0.770 is greater than -0.800.

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3 years ago
A bottle of hand lotion is on sale for $2.25. If this price represents a 50% discount from the original price,what is the origin
nalin [4]

Step-by-step explanation:

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3 0
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A train leaves at 17.22 and arrives at its destination at 18.14.
sattari [20]

Answer:

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Step-by-step explanation:

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