Given That 20=20+18+16 + . . . +X, How Many Terms Are On The Right Side Of The Equation?, Find The Sum Of 2212100201399201398201397 2013 . . . +100+10

Given that 20=20+18+16 + . . . +x, how many terms are on the right side of the equation?

Find the sum of −100–99–98–97 – . . . +100+101+102

Please answer these 2 questions.

 

Answer:

Step-by-step explanation:

Sum of arithmetic sequence:

Sn = n/2 2a₁ + (n-1)(d)

Where:

Sn = sum of the sequence

n = number of terms

a₁ = first term

d = common difference

Given:

20 = 20+18+16+...+x

Sn = 20

a₁ = 20

d = -2  (the sequence decreases by 2 per term)

x = nth term

Find n, the number of terms:

20 = n/2 2(20) + (n-1)(-2)

20 = n/2 {40 + 2 - 2n

20 = n 21 - n)

20 = -n² + 21n

Arrange the quadratic equation in standard form:

n² - 21n + 20 = 0

Factor:

(n - 20) (n - 1) = 0

n - 20 = 20

n = 20

n - 1 = 0

n = 1

Choose n = 20.

ANSWER: There are 20 terms.

Find the 20th term:

a₂₀ = 20 + (20-1)(-2)

a₂₀ = 20 + (19)(-2)

a₂₀ = 20 - 38

a₂₀ = -18

The 20th term x = -18.

Check:

Sn = n/2 (a₁ + an)

20 = 20/2 (20 + (-18))

20 = 10 (2)

20 = 20  (True)

----

Find the sum of  −100–99–98–97 – . . . +100+101+102

Where:

a₁ = -100

d = 1 (the sequence is increasing hence the common difference is positive)

an = 102

n = unknowm

Find n, the number of terms:

an = a₁ + (n-1)(d)

102 = -100 + (n-1)(1)

102 = -100 - 1 + n

102 = -101 + n

n = 102 + 101

n = 203

There are 203 terms.

Find the sum:

S₂₀₃ = 203/2 -100 + 102}

S₂₀₃ = 203/2 (2)

S₂₀₃ = 203

ANSWER: The sum is 203.


Comments

Post a Comment

Popular posts from this blog

Subjective Meaning In Spoliarium

Subjective meaning in spoliarium   Gladiator is the subject of the spoliarium painting. The picture recreates a despoiling scene in a Roman circus where dead gladiators are stripped of weapons and garments. At the center of the painting are fallen gladiators being dragged by Roman soldiers. On the left, spectators ardently await their chance to strip off the combatants of their metal helmets and other armory. In contrast with the charged emotions featured on the left, the right side meanwhile presents a somber mood. An old man carries a torch perhaps searching for his son while a woman weeps the death of her loved one. Meaning of Spoliarium Spoliarium is a Latin word referring to the basement of the Roman Colosseum where the fallen and dying gladiators are dumped and devoid of their worldly possessions. Who painted the spolarium? Spolarium is a painting done by Filipino painter Juan Luna in 1884. Juan Luna is a Filipino educated at the Academia de Dibujo y Pintura (P...
Read more

Ang Pinaka Malalim Na Dako Sa Karagatan Ay Bahaging Nasa Dulo Ng Marianas

Ang pinaka malalim na dako sa karagatan ay bahaging nasa dulo ng marianas   Answer: Tinatawag na "Challenger Deep" ang pinakamalalim na bahagi ng karagatan. Explanation: Ang Challenger Deep ay ang pinakamalalim na bahagi ng karagatan sa Daigdig. Ito ay may kalalimang nagmumula sa 10,898 metro hanggang 10,916 metro. Ito ay matatagpuan sa Karagatang Pasipiko, sa katimugang bahagi ng Mariana Trench.
Read more

Describe What Kind Of Son Or Daughter, Brother Or Sister You Are.

Describe what kind of son or daughter, brother or sister you are.   Describe what kind of son or daughter, brother or sister you are. As a daughter, I am obedient, courteous, respectful, and caring. I am a responsible daughter. I always follow what my parents say. When they say "study hard", I do. As a sister, I am caring, protective and loving. I always console them whenever they have problems. Learn more:   Pick a past experience in your life and explain how that particular incident has change you. brainly.ph/question/2126910 Code: 11.16.1.2.
Read more