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AnnZ [28]
3 years ago
9

FIND THE SUM OF 20 TERMS OF THE ARITHMETIC SERIES IN WHICH 3rd TERM IS 7 AND 7th TERM IS 2 MORE THAN THREE TIMES ITS 3rd TERM

Mathematics
1 answer:
algol133 years ago
8 0

Answer:

740

Step-by-step explanation:

The n th term of an arithmetic series is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then

a₁ + 2d = 7 → (1)

a₁ + 6d = 23 → (2)

Subtract (1) from (2) term by term

4d = 16 ( divide both sides by 4 )

d = 4

Substitute d = 4 into (1)

a₁ + 2(4) = 7

a₁ + 8 = 7 ( subtract 8 from both sides )

a₁ = - 1

The sum to n terms of an arithmetic series is

S_{n} = \frac{n}{2} [ 2a₁ + (n - 1)d ] , thus

S_{20} = \frac{20}{2} [ (2 × - 1) + (19 × 4) ]

     = 10(- 2 + 76) = 10 × 74 = 740

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Please help and explain!!!!!
FinnZ [79.3K]

Let x be the amount of the 30% alloy and y the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

x+y=100

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

0.3x+0.6y=0.54(x+y)=54

Now,

x+y=100\implies y=100-x

\implies0.3x+0.6(100-x)=54

\implies60-0.3x=54

\implies0.3x=6

\implies x=20

\implies y=100-20=80

6 0
3 years ago
In still water, a boat averages 12 miles per hour. It takes the same amount of time to travel 14 miles downstream, with the curr
anyanavicka [17]
T is equal in both situations ... d = r X t   so d/r = t
c is rate of waters current

\frac{14}{12+c} = \frac{7}{12-c}
14(12 - c) = 7(12 + c)
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24 - 2c = 12 + c
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8 0
3 years ago
Which equation could be used to solve for the value of n if n + 2 = 6?
NNADVOKAT [17]

You can use 6-2=4

You just Subtract the 2 from 6 and that gives 4

5 0
3 years ago
describe the steps you would take to determine the distance in miles between two towns that are 200 kilometers apart
MaRussiya [10]
It will be -200 kilometers because you gotta get a ruler
6 0
3 years ago
Help with math homework
Anestetic [448]
1) 65+57= 122
180-122= 58

2) 40+90=130
180-130=50

3) 130+20=150
180-150=30

4) 85+50= 135
180-135=45

Sorry, IDK the rest. So so sorry.
8 0
3 years ago
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