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andrew-mc [135]
3 years ago
9

The product of 4, and a number increased by 8, is -48

Mathematics
1 answer:
german3 years ago
8 0

Answer:

4n + 8 = -48

n = -14

Step-by-step explanation:

Using key words from the problem, you can set up an equation with the proper operations to solve for the variable.  Product = multiplication, so the 'product of 4 and a number' = 4n.  Increased = addition, so increased by 8 = 4n + 8.  The word 'is' means equal to, so:

4n + 8  = -48

In order to solve for 'n', you use inverse (opposite) operations and whatever you do to one side of the equation, you do to the other:

Subtract 8:  4n + 8 - 8 = -48 - 8 or 4n = -56

Divide 4:  4n/4 = -56/4

Solve for 'n':  n = -14

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Find the sum of the first 20 terms of an arithmetic sequence with an 18th term of 8.1 and a common difference of 0.25.
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The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Given,

18th term of an arithmetic sequence = 8.1

Common difference = d = 0.25.

<h3>What is an arithmetic sequence?</h3>

The sequence in which the difference between the consecutive term is constant.

The nth term is denoted by:

a_n = a + ( n - 1 ) d

The sum of an arithmetic sequence:

S_n = n/2 [ 2a + ( n - 1 ) d ]

Find the 18th term of the sequence.

18th term = 8.1

d = 0.25

8.1 = a + ( 18 - 1 ) 0.25

8.1 = a + 17 x 0.25

8.1 = a + 4.25

a = 8.1 - 4.25

a = 3.85

Find the sum of 20 terms.

S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]

         = 10 [ 7.7 + 19 x 0.25 ]

         = 10 [ 7.7 + 4.75 ]

         = 10 x 12.45

         = 124.5

Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Learn more about arithmetic sequence here:

brainly.com/question/25749583

#SPJ1

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