All categories

3 years ago

Compute 1 + 2 + 3 + 4 + ... +48 +49 + 50.

Mathematics

2 answers:

Maurinko [17]3 years ago

6 0

Answer: 1275

Explanation:

ad-work [718]3 years ago

4 0

Answer:

1275

Step-by-step explanation:

This is an arithmetic series. The formula for this is Sₙ = (n/2)(a₁ +aₙ)d. a₁ is the first term, so here it is 1, and aₙ is the nth term, or the last term, which is 50 here, but we don't know n.

Now we have to use the equation for an arithmetic sequence to solve for n. A sequence would just be if there was not a last number and it went on forever. that equation looks like aₙ = a₁ + (n - 1)d. Now the only new variable is d, which is the common difference. You can find that by subtracting one term from the term before it, like 2-1 = 1, so d is 1.

We can now solve for n by plugging our numbers into the second equation, so 50 = 1 + (n - 1)1, we can distribute the 1 and to (n-1) and get 50 = 1 + n - 1. Now the ones will cancel and we are left with n = 50

Finally we can plug everything into our original equation and find Sₙ = (50/2)(1+50), which simplifies to Sₙ = 25(51), and Sₙ = 1275.

You might be interested in

Find an equation of the hyperbola having foci at (-9,-4) and (7,-4) and vertices at (-6, -4) and (4.-4).

Veronika [31]

Answer:

-9,-4

Step-by-step explanation:

6 0

3 years ago

Please help me understand and explain it to me please.<br><br>Recursive Sequence Function

DedPeter [7]

A recursive sequence is a sequence of numbers whose values are determined by the numbers that come before them in the sequence.

We’re given a sequence whose (n + 1)-th term f(n + 1) depends on the value of the n-th term f(n), specified by the recursive rule

f(n + 1) = -4 f(n) + 3

We’re also given the 1st term in the sequence, f(1) = 1. Using this value and the recursive rule, we can find the next term f(2). (Just replace n with 1.)

f(1 + 1) = -4 f(1) + 3

f(2) = -4 • 1 + 3

f(2) = -1

We do the same thing to find the next term f(3) :

f(2 + 1) = -4 f(2) + 3

f(3) = -4 • (-1) + 3

f(3) = 7

One more time to find the next term f(4) :

f(3 + 1) = -4 f(3) + 3

f(4) = -4 • 7 + 3

f(4) = -25

4 0

2 years ago

One of the Same side angles of two parallel lines is 60° greater than the other. Find the two angles.

BARSIC [14]

Answer:

60,120

Step-by-step explanation:

We know that angles on the same side of the transversal always add up to 180 ( are supplementary)

Hence, taking one of the angles as x we get,

x+(60+x)=180

2x+60=180

2x=120

x=60

Hence, one angle is 60 degrees while the other 120 degrees

4 0

3 years ago

(2x + 35)=(5x-22) what’s x

finlep [7]

Answer:

x=19

Step-by-step explanation:

5 0

3 years ago

Consider the following system of equations. -10x2-10y2=-300 5x2+5y2=150 Which statement describes why the system has infinite so

scoundrel [369]

Answer:

The equations represent circles that result in the same graph.

Step-by-step explanation:

we have

$-10x^{2}-10y^{2}=-300$

Divide by -10 both sides

$x^{2}+y^{2}=30$ -----> equation A

This is the equation of a circle centered at origin with radius $r=\sqrt{30} \ units$

and

$5x^{2}+5y^{2}=150$

Divide by 5 both sides

$x^{2}+y^{2}=30$ -----> equation B

This is the equation of a circle centered at origin with radius $r=\sqrt{30} \ units$

equation A and equation B are equal

therefore

The system has infinite solutions, because the equations represent circles that result in the same graph.

4 0

3 years ago

Compute 1 + 2 + 3 + 4 + ... +48 +49 + 50.​

Compute 1 + 2 + 3 + 4 + ... +48 +49 + 50.