Question

Can someone please help me with one or both of these problems, I'm so confused but the assignment is due soon!!

Answer 1

Answer:

First question: 1270

Second question: 4080

Step-by-step explanation:

Here is the Sum formula:

$S_{n}=\frac{n}{2}(a_{1}+a_{n})$

where n represents the number of terms, and

$a_{1}$ is the first term, and $a_{n}$ 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 ($a_{1}$) by substituting k in the formula for 5.

3(5)+26=15+26=41

You can find the last term ($a_{n}$) by substituting k for 20 into the formula.

3(20)+26=60+26=86

now, knowing there are 20 terms in total, $a_{1} =41$, and $a_{n} =86$, we can put it into the Sum formula.

$S_{20}= \frac{20}{2} (41+86)$

$S_{20}= \frac{20}{2} (127)$

$S_{20}= 10 (127)$

$S_{20}= 1270$

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:

$S_{20}= \frac{20}{2} (99+309)$

$S_{20}= \frac{20}{2} (408)$

$S_{20}= 10(408)$

$S_{20}=4080$

Answer to the second question: 4080