Answer:
First question: 1270
Second question: 4080
Step-by-step explanation:
Here is the Sum formula:
[tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})[/tex]
where n represents the number of terms, and
[tex]a_{1}[/tex] is the first term, and [tex]a_{n}[/tex] is the last term.
Let's look at the first question:
k is the first number of the sequence, 5, and 20 is the last number of the sequence.
You can find the first term ([tex]a_{1}[/tex]) by substituting k in the formula for 5.
3(5)+26=15+26=41
You can find the last term ([tex]a_{n}[/tex]) by substituting k for 20 into the formula.
3(20)+26=60+26=86
now, knowing there are 20 terms in total, [tex]a_{1} =41[/tex], and [tex]a_{n} =86[/tex], we can put it into the Sum formula.
[tex]S_{20}= \frac{20}{2} (41+86)[/tex]
[tex]S_{20}= \frac{20}{2} (127)[/tex]
[tex]S_{20}= 10 (127)[/tex]
[tex]S_{20}= 1270[/tex]
Answer to the first question: 1270
Next question:
Even though the given formula uses n as the variable, this problem works the same way as the previous one.
Substitute n in the formula for k, which is 5 to find the first term: 14(5)+29=99
Substitute 20 for n to find the second term: 14(20)+29=309
Now assemble the Sum formula:
[tex]S_{20}= \frac{20}{2} (99+309)[/tex]
[tex]S_{20}= \frac{20}{2} (408)[/tex]
[tex]S_{20}= 10(408)[/tex]
[tex]S_{20}=4080[/tex]
Answer to the second question: 4080
