Certainly! Let's address the problem step by step.
### Question 4
The given recurrence relation for a sequence is:
[tex]\[
a_n = a_{n-1} + 17.4
\][/tex]
and the first term [tex]\(a_1\)[/tex] is given by:
[tex]\[
a_1 = 9
\][/tex]
You are also given the duration over which these effects accumulate, which is 4 days (e.g., Monday to Thursday).
To solve this, we'll first find the values of the sequence for the first four terms and then determine the specified sequence values.
### Step-by-Step Solution:
Step 1: Calculate the first term [tex]\(a_1\)[/tex]
[tex]\[
a_1 = 9
\][/tex]
Step 2: Calculate the subsequent terms using the recurrence relation [tex]\(a_{n} = a_{n-1} + 17.4\)[/tex]
For [tex]\(a_2\)[/tex]:
[tex]\[
a_2 = a_1 + 17.4 = 9 + 17.4 = 26.4
\][/tex]
For [tex]\(a_3\)[/tex]:
[tex]\[
a_3 = a_2 + 17.4 = 26.4 + 17.4 = 43.8
\][/tex]
For [tex]\(a_4\)[/tex]:
[tex]\[
a_4 = a_3 + 17.4 = 43.8 + 17.4 = 61.2
\][/tex]
Thus, the first four terms of the sequence are [tex]\(9, 26.4, 43.8, 61.2\)[/tex].
### Final Calculation:
Now, using these terms, we can sum them and calculate various means as needed.
[tex]\[
\text{Sum of the first 4 terms} = 9 + 26.4 + 43.8 + 61.2 = 140.4
\][/tex]
Let's determine the total additional effect over these 4 days:
The initial value [tex]\(a_1\)[/tex] adds to the total, followed by additive steps for each subsequent day:
[tex]\[
\text{Total additional effect} = (a_2 - a_1) + (a_3 - a_2) + (a_4 - a_3) = 17.4 + 17.4 + 17.4 = 52.2
\][/tex]
### Conclusions:
1. The total increase over these 4 days (addition due to daily computation) is [tex]\(52.2\)[/tex].
2. The total number of computers after these 4 days starting from [tex]\(9\)[/tex] will be:
[tex]\[
a_4 = a_1 + \text{total increase} = 9 + 52.2 = 61.2
\][/tex]
Using 52.2 as [tex]\( \text{total additional computers} \)[/tex] and 61.2 as [tex]\( \text{total computers} \)[/tex].
