All categories

3 years ago

What is the sum of the first 51 terms of the sequence? −282,−266,−250,−234,...

Mathematics

1 answer:

Pavel [41]3 years ago

8 0

Answer:

The sum of the first 51 terms of the sequence is 6018

Step-by-step explanation:

AP: −282,−266,−250,−234,...

First term = a = -282

Common difference = d = $a_2-a_1=a_3-a_2$

Common difference = d = -266-(-282)=-250-(-266)=16

Formula of sum of first n terms = $S_n=\frac{n}{2}(2a+(n-1)d)$

Substitute n = 51

So, $S_{51}=\frac{51}{2}(2(-282)+(51-1)(16))$

$S_{51}=6018$

Hence the sum of the first 51 terms of the sequence is 6018

You might be interested in

For f(x) = 2x+1 and g(x) = x2 - 7, find (f+ g)(x).

____ [38]

Answer:

the answer is A. it good answer

5 0

3 years ago

Ignore the stuff around it ,could someone explain me this?

Ierofanga [76]

Answer:

The lines blue and green are perpendicular

Step-by-step explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope of the blue line

we have the points

(-1,-3) and (0,3)

substitute

$m=\frac{3+3}{0+1}$

$m=\frac{6}{1}=6$

step 2

Find the slope of the red line

we have the points

(3,-3) and (4,2)

substitute

$m=\frac{2+3}{4-3}$

$m=\frac{5}{1}=5$

step 3

Find the slope of the green line

we have the points

(-4,-1) and (2,-2)

substitute

$m=\frac{-2+1}{2+4}$

$m=-\frac{1}{6}$

step 4

Compare the slopes

Blue line ----> $m=6$

Red line ----. $m=5$

Green line ---> $m=-\frac{1}{6}$

The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)

therefore

The lines blue and green are perpendicular

7 0

3 years ago

1-tanA÷1+tanA=1-sin2A÷cos2A

Aleksandr-060686 [28]

hope u get it. I've used RHS to prove LHS

7 0

3 years ago

In preperation for an easter egg hunt, 4 blue eggs are filled for every 7 green. How many green eggs will be filled if 100 blue

ivann1987 [24]

Answer:

1. Typed question: 175 green eggs

2. Attached: 22 tables

Step-by-step explanation:

For the question you typed down, it is a ratio and proportion problem. You need to solve for the ratio proportional to the first ratio given.

4 blue eggs are filled for every 7 green. This means that the ratio between blue eggs and green eggs is 4:7.

Now yo need to figure out a ratio proportional to 4:7 if 100 blue eggs were filled. Below is how this is set up:

$\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}$

Now let's solve for x:

$\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}\\\\or\\\\\dfrac{4}{7}=\dfrac{100}{x}\\\\Cross-multiply\\\\4x = (7)(100)\\\\4x = 700\\\\Divide\;both\;sides\;by\;4\\\\\dfrac{4x}{4}=\dfrac{700}{4}\\\\x=175$

For your attached problem:

You have a total of 175 people, you need to figure out how many round tables you need if here are 8 chairs for each table You just need to divide the number of people by the number of chairs per table.

175 ÷ 8 = 21.9 tables

Now since you cannot have half a table, you round up to the nearest whole number. (we round up because you need to make sure that all of them are seated)

21.9 ≅ 22 tables.

8 0

4 years ago

Madi has 5 apples and 15 oranges. what is a true statement

AlexFokin [52]

Answer:

The true statement is that the answer is 75

Step-by-step explanation:

7 0

3 years ago