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
STALIN [3.7K]
3 years ago
15

Generate the nest three terms of each arithmetic sequence shown below.

Mathematics
1 answer:
o-na [289]3 years ago
4 0

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

<u>A)a1=-2 and d=4</u>

We know that the arithmetic sequence formula is

a_{n}=a_{1}+(n-1)d

Now

a_{2}=a_{1}+(2-1)d

a_{2}=a_{1}+(1)d

Substituting the given value we get

a_{2}= -2+(1)4

a_{2}= -2+4

a_{2}= 2

------------------------------------------

Similarly

a_{3}=a_{1}+(3-1)d

a_{3}=a_{1}+(2)d

Substituting the given value we get

a_{3}= -2+(2)4

a_{3}= -2+8

a_{3}= 6

-------------------------------------------------

a_{4}=a_{1}+(4-1)d

a_{4}=a_{1}+(3)d

Substituting the given value we get

a_{4}= -2+(3)4

a_{4}= -2+16

a_{4}= 10

-------------------------------------------------------------------------------------------

<u>B</u><u>  a_n=a_{(n-1)}-8  with a_1=10</u>

a_2=a_{(2-1)}-8

a_2=a_{1}-8

Substituting the given value

a_2= 10-8

a_2=2

---------------------------------------------------------------------

a_3=a_{(3-1)}-8

a_3=a_{2}-8

Substituting the  value

a_3=2-8

a_3= -6

---------------------------------------------------------------------

a_4=a_{(4-1)}-8

a_4=a_{3}-8

Substituting the  value

a_4= -6-8

a_4= -14

-------------------------------------------------------------------------------------------

<u>C) a_1=3, a_2=1</u>

Here the difference is -2

the arithmetic sequence formula is

a_{n}=a_{1}+(n-1)d

Now

a_{3}=a_{1}+(3-1)d

a_{3}=a_{1}+(2)d

Substituting the value we get

a_{3}= 3+(2)-2

a_{3}= 3-4

a_{3}= -1

------------------------------------------------------------------------------

a_{4}=a_{1}+(4-1)d

a_{4}=a_{1}+(3)d

Substituting the value we get

a_{4}= 3+(3)-2

a_{4}= 3-6

a_{4}= -3

----------------------------------------------------------------------------------

a_{5}=a_{1}+(5-1)d

a_{5}=a_{1}+(4)d

Substituting the value we get

a_{5}= 3+(4)-2

a_{5}= 3-8

a_{5}= -5

You might be interested in
Help me to prove the given below. Thank you in advance
sleet_krkn [62]

Answer:

Construct MO, where O is the midpoint of CG. (As shown in the attached figure)

(1) LM = MG //given, CM is the median to the hypotenuse      

(2) CO = OG // construction    

(3) MO is a mid-segment   //(1), (2) , Definition of a mid-segment

(4) MO // LC //triangle mid-segment theorem    

(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)

(6) m∠LCO=90°  //given, ΔLCG is a right triangle

(7) m∠MOG=90° //(5), (6), definition of congruent angles

(8) m∠MOC=180° – 90° = 90° // linear pair

(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles

(10) MO=MO //common side, reflexive property of equality  

(11) ΔMCO ≅ ΔMGO  //(2), (9), (10) Side-Angle-Side postulate

(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)      

(13) MG= ½LG // Given, CM is the median to the hypotenuse    

(15) MC = ½LG //(12) , (13), substitution  

8 0
3 years ago
Angle Side Relationship 1/5<br> Will mark brainlist to whoever answers first
tresset_1 [31]

Answer:

m<A > m<B > m<C

Step-by-step explanation:

In triangles, the measure of angles is proportional with the side length's they see,

The angle with the biggest the biggest measure sees the biggest side length

in triangle ABC the side lengths are given as

BC = 14, CA = 13 and AB = 5

from this, we can conclude:

m<A > m<B > m<C

3 0
1 year ago
How many fractions are there between any two numbers on a number line?
klasskru [66]

Answer:

There are an infinite number of fractions in between numbers on a number line.

Step-by-step explanation:

The reason for this is because we have an infinite number of denominators to use. Therefore, we can not number the amount we use.

4 0
3 years ago
Read 2 more answers
Can anyone help me with this? I will mark you as brainliest
creativ13 [48]

Answer:

6×6×6×6×6×6×6=279936

6×6×6×6×6=7776

279936÷7776= 36

36 is the answer but u could express it as: (6²)....Six squared

Step-by-step explanation:

4 0
3 years ago
Find the perimeter of a triangle that has 3 equals sides each 6 centimeters long
aleksandrvk [35]

Answer:

18 centimeters

Step-by-step explanation:

The formula for finding the perimeter is side + base+side . There for you do 6+6+6

that gives you 18

5 0
2 years ago
Other questions:
  • Eight hundred tickets are sold for a play. Thirty-five percent of those tickets were sold in advance. Which equation can be used
    10·1 answer
  • Find the coordinate of T' after a 90° counterclockwise rotation of the triangle about the origin and then a translation of 3 uni
    14·1 answer
  • Write the following mixed decimal as a mixed number and reduce to the lowest term 17.46 92.004
    5·1 answer
  • Find the perimeter of the square shown below:<br> Area = 49 cm2 plz!! It’s due in 5 minutes!!!!!!!
    9·1 answer
  • Which expression is equivalent to the given expression?
    9·1 answer
  • HELP PLS WILL MARK BRAINLIEST!!!!!!!!!!!!
    9·1 answer
  • F(x) = 2x<br> g(x) = 2x + 1<br> Find<br> (f/g) (x) . Include ahy restrictions on the domain.
    8·1 answer
  • Please I need help. Help me please​
    5·1 answer
  • graph the linear equation. find three points that solve the equation, then plot them on the graph. 5x-4y=-18
    10·1 answer
  • Two groups of tourists are on the same floor of a skyscraper they are visiting, and they board adjacent elevators at the same ti
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!