No tricks or anything. just an answer. given the explicit rule, e(n)=5n-2, what are the first 5 terms of the sequence? also, is the problem linear or non-linear

Answers:
The first five terms are: 3, 8, 13, 18, 23
This is a linear sequence



Explanation:

Plug in n = 1 to get the first term
E(n) = 5*n-2
E(1) = 5*1-2
E(1) = 3
So 3 is the first term

Do the same for n = 2 to get the second term
E(n) = 5*n-2
E(2) = 5*2-2
E(2) = 8
So 8 is the second term

And again for n = 3
E(n) = 5*n-2
E(3) = 5*3-2
E(3) = 13
This means 13 is the third term

And again for n = 4
E(n) = 5*n-2
E(4) = 5*4-2
E(4) = 18
This means 18 is the fourth term

Finally, repeat for n = 5
E(n) = 5*n-2
E(5) = 5*5 - 2
E(5) = 23
So 23 is the fifth term

This sequence is linear because we're incrementing by the same amount each time. In this case, we're adding 5 each time for the sequence 3, 8, 13, 18, 23, and so on.

30 desks

200 bookcases

Step-by-step explanation:

Hello!

To solve this problem we must propose 2 linear equations as follows.

1.for the cutting time = if we multiply the number of desks (D) by the cutting time (5h) plus the number of bookcases (B) by the cutting time (15min = 0.25h), it will result in the Total available cutting time = 200h

1.For the time of the assembly = if we multiply the number of desks (D) by the time of assembly (10h) plus the number of bookcases (B) by the time of assembly (1h), it will result in the total time available of assembly = 500h.

taking into account the above we infer the following equations

5D+0.25B=200  (ecuation number 1)

10D+B=500         (ecuation number 2)

Now what we have to do is solve the system of two linear equations and two unknowns, for which we will take equation number 1 multiply it by four and subtract equation 2, then apply algebra

4(1)-(2)

20D+B=800

-

10D+B=500

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10D=300

Now we use equation number 2 to find the number of book cases

10D+B=500  

B=500-10D

B=500-10(30)=200bookcases