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Anna35 [415]
3 years ago
12

Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37

Mathematics
1 answer:
Mandarinka [93]3 years ago
6 0

Answer:

The general rule is a_n = -2 - 5(n-1)

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

a_{n} = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

a_n = a_m + (n-m)d

a3 = -12 and a8 = -37

First we find the common difference. So

a_n = a_m + (n-m)d

a_8 = a_3 + (8-3)d

-37 = -12 + 5d

5d = -25

d = -\frac{25}{5}

d = -5

So

a_n = a_1 - 5(n-1)

Finding the first term:

a_n = a_1 - 5(n-1)

Since a_3 = -12

a_n = a_1 - 5(n-1)

a_3 = a_1 - 5(3-1)

a_1 = a_3 + 10 = -12 + 10 = -2

So the general rule is:

a_n = a_1 - 5(n-1)

a_n = -2 - 5(n-1)

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11=                                                 d5
10=                                                        d5
9=                                       d4
8=                                             d4  d5
7=                          d3
6=                                d3  d4
5=             d2
4=                  d2    d3
3=  d1
2=       d1  d2
1=
0=  d1




6 0
3 years ago
Number of seconds equal to 1/5 hour
kirill115 [55]
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8 0
3 years ago
Read 2 more answers
Solve the following:<br> 6(2x+3)-3(x-2)=6
REY [17]

The value of x is -2

Step-by-step explanation:

Given that

6 (2x + 3) - 3(x - 2) = 6

Expand the bracket                    

6 (2x + 3) - 3(x - 2) = 6

12x + 18 - 3x + 6 = 6

Collect like terms

12x - 3x = 6 - 6 - 18

9x = -18

Divide through by 9

9x / 9 = -18 / 9

x = -2

Therefore, the value of x is -2

Learn more about inequality here : brainly.com/question/20252161

4 0
2 years ago
Read 2 more answers
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