I how to solve this problem

Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20

Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

$\displaystyle S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

$x_n=4-8(n-1)$

Then the last or 20th term is:

$x_{20}=4-8(20-1)=4-8(19)=-148$

Therefore, the sum of the first 20 terms are:

$\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}$

5 0

3 years ago

Read 2 more answers

Can you please help me

andrezito [222]

Answer:

its kinda dificult to explain (easier to show) but ill do my best

Step-by-step explanation:

so for part a you wanna start from the bottom (min) and go acros to the line above 1 then go three lines up for cookies. you should be on 3, 1

for part b its c lin decorates 21 cookies in 7 min

7 0

3 years ago

What 223 x 12 explain

geniusboy [140]

Answer: 2676

Step-by-step explanation:

223 x 12 = 2676

This is because 223 12 times equals 2676.

*I will attach my work for the problem so you can see the solving process more clearly :).

Hope this helps :).

4 0

2 years ago

Is 11/2 and 6/11 equivalent? Plz I need the help☹️

trapecia [35]

For this case we have the following fractions:

$\frac {11} {2}\\\frac {6} {11}$

We must rewrite the fractions, using the same denominator.

We have then:

We multiply the first fraction by 11 in the numerator and denominator:

$\frac {11} {2} \frac {11} {11}$

We multiply the second fraction by 2 in the numerator and denominator:

$\frac {6} {11} \frac {2} {2}$

Rewriting we have:

For the first fraction:

$\frac {121} {22}$

For the second fraction:

$\frac {12} {22}$

We note that:

$\frac {121} {22}> \frac {12} {22}$

Answer:

The fractions are not equivalent:

$\frac {11} {2}> \frac {6} {11}$

5 0

3 years ago

What is h−(−2.22)=−7.851 someone please help me

telo118 [61]

Answer:

h=-10.071?

Step-by-step explanation:

7 0

3 years ago