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vitfil [10]
3 years ago
13

Determine the indicated term in the following arithmetic sequences.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
5 0

Answer:

a_5= 14

a_{20}= 80

a_{18}= 340

Step-by-step explanation:

Solving (a):

We have:

a_1=2 --- first term

d = 5 -2 = 3 common difference

The 5h term is:

a_n= a_1 + (n - 1)d

a_5= 2+ (5 - 1)*3

a_5= 14

Solving (b):

We have:

a_1 = 4 --- first term

d = 8 -4 = 4 common difference

The 20h term is:

a_n= a_1 + (n - 1)d

a_{20}= 4+ (20 - 1)*4

a_{20}= 80

Solving (c):

We have:

a_1 = 0 --- first term

d = 20 -0 = 20 common difference

The 18th term is:

a_n= a_1 + (n - 1)d

a_{18}= 0+ (18 - 1)*20

a_{18}= 340

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kumpel [21]

Answer:

The required piece-wise linear function is

\left\{\begin{matrix}1.5x & 0\leq x

Step-by-step explanation:

Consider the provided information.

Let x represents the number of hours and S(x) represents the depth of snow.

There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per.

That means the depth of snow will be:

S(x)=1.5x\ \ \ 0\leq x< 4

At  4:00 a.m., it starting falling at a constant rate of 3 inches per hour,

From mid night to 4:00 a.m the depth of snow will be 1.5×4=6 inches.

If we want to calculate the total depth of snow from midnight to 7:00 am we need to add 6 inches in 3(x-4) where 4≤x<7

Therefore,

S(x)=3(x-4)+6\ \ \ 4\leq x

7:00 a.m. to 9:00 a.m., snow was  falling at a constant rate of 2 inches per hour.

From mid night to 7:00 a.m the depth of snow will be 3(7-4)+6=15 inches.

If we want to calculate the total depth of snow from midnight to 9:00 am we need to add 15 inches in 2(x-7) where 7≤x≤9

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