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
irina1246 [14]
2 years ago
12

Dont really understand how to do this

Mathematics
1 answer:
bija089 [108]2 years ago
6 0

Answers:

t_{10} = -22 \ \text{ and } S_{10} = -85

========================================================

Explanation:

t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4

and so on. This process may take a while to reach t_{10}

There's a shortcut. The nth term of any arithmetic sequence is

t_n = t_1+d(n-1)

We plug in t_1 = 5 \text{ and } d = -3 and simplify

t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8

Then we can plug in various positive whole numbers for n to find the corresponding t_n value. For example, plug in n = 2

t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2

which matches with the second term we found earlier. And,

tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}

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

The notation S_{10} refers to the sum of the first ten terms t_1, t_2, \ldots, t_9, t_{10}

We could use either the long way or the shortcut above to find all t_1 through t_{10}. Then add those values up. Or we can take this shortcut below.

Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}

The sum of the first ten terms is -85

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

As a check for S_{10}, here are the first ten terms:

  • t1 = 5
  • t2 = 2
  • t3 = -1
  • t4 = -4
  • t5 = -7
  • t6 = -10
  • t7 = -13
  • t8 = -16
  • t9 = -19
  • t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that S_{10} = -85 is correct.

You might be interested in
Express the following as standard numbers:
Ksenya-84 [330]

Answer:

A. 56,000

B. 784,000,000

C. 620

D. 0.00000432

Step-by-step explanation:

{ \tt{}}

5 0
3 years ago
In the reaction _S +3O2 → 2SO3, what coefficient should be placed in front of the S to balance the reaction? i need the answer.
sukhopar [10]

Answer:

you momma

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
dexamethasone 4 mg/1 ml is available. the MD orders 6000 mcg. how much will the nurse give? (Round to the tenth)​
aleksley [76]

Answer:

  1.5 mL

Step-by-step explanation:

The abbreviation mcg stands for "microgram," or 10^-6 grams. The abbreviation mg stands for "milligram," or 10^-3 grams. The relationship between these is ...

  1 mg = 1000 mcg

<h3>Dose</h3>

The order for 6000 mcg is an order for 6(1000 mcg) = 6(1 mg) = 6 mg. At 4 mg/mL, the quantity of dexamethasone required is ...

  (6 mg)/(4 mg/mL) = (6/4) mL = 1.5 mL

The nurse will give 1.5 milliliters of dexamethasone.

4 0
1 year ago
2x+7 =5 is an example of...
tresset_1 [31]

Answer:

This is an example of distribution

Step-by-step explanation:

The reason why is because the equation is linear and if you exclud the y it show that it can distribute.

6 0
3 years ago
40 PONITS
Alex787 [66]

Hence, second option is the true option.                            {Result of spin, card color}

{Green, Purple} {Yellow, Purple}  {Purple, Purple }

{Green, Green}  {Yellow, Green}  {Purple, Green}

Step-by-step explanation:

It is given that:

A spinner with 3 equal sectors is shown in the figure. The colors Green, Yellow, and Purple are marked on it.

Two cards are shown on the right side. Their colors are Purple and Green.

The table that identifies the sample space of spinning the spinner and then selecting  a card is:

     {Result of spin, card color}

{Green, Purple} {Yellow, Purple}  {Purple, Purple }

{Green, Green}  {Yellow, Green}  {Purple, Green}

( Since in rest of the options the red color in the sample space but there is no card or no such color in the spin which is red)

6 0
2 years ago
Read 2 more answers
Other questions:
  • Danielle will use the instructions in the box below to make a cleaning solution I
    11·1 answer
  • HELP PLEASE!!! SHOW ALL YOU WORK PLEASE HELP HELP HELP PLEASE
    15·1 answer
  • Let x represent the year and y represent the amount of sales, in millions of dollars, in the regression equation.
    13·1 answer
  • (1 pt) Lucas cut a board that is ft long and ft wide. What is the area of the board? Express your answer in simplest form. A. sq
    12·1 answer
  • what do you think is the most important advantage, privilege, or benefit that men enjoy in the United States?
    7·1 answer
  • Ismail tried to prove that sin(θ) = cos(90°− θ) using the following diagram. His proof is not correct.
    9·1 answer
  • Which number best represents the slope of the graphed line?
    9·1 answer
  • 40 of the cats at the pet store are black, which is 25% of all cats. How many cats are there at the pet store
    14·2 answers
  • Find the distance between. the points (-1,-2) and (-2,0 round too the nearest hundredth
    5·1 answer
  • -2-(-5) = -2 + (-5)<br> 2- =
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!