1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
GarryVolchara [31]
3 years ago
10

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 34 terms?

Mathematics
2 answers:
gladu [14]3 years ago
8 0
I believe its 3,468.
Naily [24]3 years ago
3 0
Notice that the difference between 2 consecutive terms is 6,

Let a_n mean the n'th term of the sequence, so:

a_1=3,
a_2=a_1+6=3+6=9,  
a_3=a_2+6=9+6=15

The sequence is "arithmetic" means that every term, is its previous term + 6, the common difference.

So the sequence is 3, 9, 15, 21, 27, ....

write again each term of the sequence to see how we get it, so that we are able to figure out a general formula:

a_1=3

a_2=3+6

a_3=[3+6]+6

a_4=[3+6+6]+6


a_5=[3+6+6+6]+6
.
.
so we notice that to find the 6.th term we need to add 5 sixes to 3.
                            to find the 7.th term we add 6 sixes to 3, 

In general, to find the n.th term, we add (n-1) sixes to 3
 
Thus, the general formula is  a_n=3+6(n-1), 


The sum of the first 34 terms of the sequence is 

a_1+a_2+a_3+ ..... + a_3_3+a_3_4=

3 + (3+6*1)+(3+6*2)+(3+6*3)+...+(3+6*33)=

3*34+(6*1+6*2+...6*33)=102+6(1+2+3+4+...+33)


the sum of the first A consecutive numbers 1+2+3+4+...+A is equal to :

A(A+1)/2 ,  according to the famous Gauss formula, 

so 1+2+3+...+33= 33(33+1)/2=(33*34)/2=17*33=561


Thus, 102+6(1+2+3+4+...+33)= 102+6*561=102+ 3366=3,468


Answer:  D)  3,468 



You might be interested in
A 12-foot wire supports a tree creating a 48 degreee angle. What is the closest distance up the tree that the wire reaches?
BartSMP [9]

The closest distance up the tree where the wire reaches is 17.93 foot.

<u>Explanation:</u>

Given-

Length of the wire, L = 12 foot

angle, Ф= 48°

Distance upto which the wire reaches the tree, x = ?

We know,

cos Ф = base/ hypotenuse

cos 48° = 12/ x

0.669 = 12/x

x = 17.93 foot

Therefore, the closest distance up the tree where the wire reaches is 17.93 foot.

5 0
3 years ago
1) 6=A/4+2 can someone help please
monitta

Answer:

A=16

Step-by-step explanation:

6=A/4+2

-2       -2

4=A/4

x4  x4

16=A

6 0
3 years ago
Which statement is true about the circumference of a circle? The circumference is equal to the radius of the circle. The circumf
Irina18 [472]
<h3>The true statement about circumference of a circle is:  circumference is found by multiplying Pi by the diameter</h3>

<em><u>Solution:</u></em>

<em><u>The circumference of a circle is given as:</u></em>

\text{circumference } = 2 \pi r

Where,

"r" is the radius of circle

We know that,

diameter = 2 \times radius\\\\d = 2 \times r\\\\d = 2r

<em><u>Thus the circumference can also written as:</u></em>

\text{circumference } = 2 \pi r\\\\\text{circumference } = \pi \times d

Thus, the circumference is found by multiplying Pi by the diameter is correct statement

7 0
3 years ago
Read 2 more answers
Fide f (-7) evaluate the function
pychu [463]

Step-by-step explanation:

f(x)=-x²+8x

By replacing x with -7, we get

f(-7)=-(-7)²+8×(-7)

=-49-56

=-105

5 0
2 years ago
Read 2 more answers
35 POINTS PLEASE SOMBODY ANSWER THESE ARE mY lASSST POINTSSS<br> **also please look at both pics.
aleksley [76]

Step-by-step explanation:

2x + 2(3x - 1) = 3(x + 1) \\ 2x + 6x - 2 = 3x + 3 \\ 8x - 2 = 3x + 3 \\ 8x - 3x = 3 + 2 \\ 5x = 5 \\ x = 1inch

perimeter \: of \: rectangle \\ 2x + 2(3x - 1) \\  = 2(1) + 2(3(1) - 1) \\  = 2 + 2(2) \\  = 6 \: inches

perimeter \: of \: \: triangle \\ 3(x + 1) \\  = 3(1 + 1) \\  = 3(2) \\  = 6 \: inches

3 0
3 years ago
Other questions:
  • Five times a number plus 5 has the same value as twice the number plus 10
    9·1 answer
  • Can you plz find the area of the parallelogram??
    7·2 answers
  • Allie needs 65 centimeters of fabric for the pillow she is making. the fabric costs $4.20 for a meter and the stuffing for pillo
    5·1 answer
  • Y2 + 8zx - 2xy -4yz factorise ?
    6·1 answer
  • If the ratio of the edges of two cubes is 3:2, what is the ratio of the volume of the larger cube to the volume of the smaller o
    13·1 answer
  • Micaela works in a department store selling clothing. She makes a guaranteed salary
    5·1 answer
  • What’s the equation for this graph?
    5·1 answer
  • What is the slope?????????
    13·1 answer
  • Find the slope from the table​
    8·1 answer
  • Find the area of this circle please…Use 3 for pi
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!