Answer:
First question: 1270
Second question: 4080
Step-by-step explanation:
Here is the Sum formula:
![S_{n}=\frac{n}{2}(a_{1}+a_{n})](https://tex.z-dn.net/?f=S_%7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D%28a_%7B1%7D%2Ba_%7Bn%7D%29)
where n represents the number of terms, and
is the first term, and
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 (
) by substituting k in the formula for 5.
3(5)+26=15+26=41
You can find the last term (
) by substituting k for 20 into the formula.
3(20)+26=60+26=86
now, knowing there are 20 terms in total,
, and
, we can put it into the Sum formula.
![S_{20}= \frac{20}{2} (41+86)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%20%5Cfrac%7B20%7D%7B2%7D%20%2841%2B86%29)
![S_{20}= \frac{20}{2} (127)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%20%5Cfrac%7B20%7D%7B2%7D%20%28127%29)
![S_{20}= 10 (127)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%2010%20%28127%29)
![S_{20}= 1270](https://tex.z-dn.net/?f=S_%7B20%7D%3D%201270)
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:
![S_{20}= \frac{20}{2} (99+309)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%20%5Cfrac%7B20%7D%7B2%7D%20%2899%2B309%29)
![S_{20}= \frac{20}{2} (408)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%20%5Cfrac%7B20%7D%7B2%7D%20%28408%29)
![S_{20}= 10(408)](https://tex.z-dn.net/?f=S_%7B20%7D%3D%2010%28408%29)
![S_{20}=4080](https://tex.z-dn.net/?f=S_%7B20%7D%3D4080)
Answer to the second question: 4080