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MaRussiya [10]
3 years ago
5

Question

Mathematics
1 answer:
joja [24]3 years ago
6 0

Answer:

The recursive rule is f(1) = first term;  f_({n}) = f_({n-1}) + d

f(1) = 55;  f_{20} = f_{19}  + 10

The explicit rule is f(n) = f(1) + (n - 1)d

f(20) = 245

Step-by-step explanation:

The recursive rule of the arithmetic sequence is

a_{1} = first term;   a_{n} = a_{n-1}  + d

Where:

  • a_{1} is the first term in the sequence
  • a_{n} is the nth term in the sequence  
  • a_{n-1} is the term before the nth term  
  • n is term number
  • d is the common difference.

The explicit rule of the arithmetic sequence is

a_{n}=a_{1}+(n-1)d

where:

  • a_{1} is  the first term in the sequence
  • a_{n} is the nth term in the sequence  
  • n is term number
  • d is the common difference

∵ The first 4 terms of the sequence are 55, 65, 75, 85

∴ a_{1} = 55

∵ d = 65 - 55

∴ d = 10

∵ We need to find the 20th term

∴ n = 20

∵ The recursive rule is f(1) = first term;  f_({n}) = f_({n-1}) + d

→ Substitute the values of a_{1}, n, and d in recursive rule

∴ f(1) = 55;  f_{20} = f_{19}  + 10

∵ The explicit rule is f(n) = f(1) + (n - 1)d

→ Substitute the values of n and d to find it

∴ f(20) = 55 + 19(10) = 245

∴ f(20) = 245

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Solving a system of equations we will see that we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.

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First, we need to define the variables:

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Replacing that in the other equation:

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