the different between the third term and first term of a geometric progression is 42 if the fourth is greater than the second term by 168. find the first term
Whoever ("answered") is answering these questions immediately and incorrectly is not helping the students one little bit.
Not only that, but my correct solutions, which I had posted with my regular name have been deleted.
Show me a possible title and the factors and setting of:
"The stone walls were tall, the castle of Gazeward: that ancient fortress built into the mountains rock was being overrun, green-skinned orcs hurried through the corridors slaying both men and women and even worse, children. No one was exempt from the black orcish blade. Tyri the king of the dying people, made a resolve to protect his people and die fighting. He fought of six orcs at a time, throwing their lifeless corpses to the ground.
The orcs feared him and would have fled away, but they beheld their leader Iros, coming forward with his magical whip to draw blood from any who fled, the orcs in fear of his savagely attacked the king.
He fought like a true knight but at last, he was thrown down and his head removed. Iros placed it upon a spear shaft and held it aloft so that all might see it."
Title: The Fall of Gazeward Castle: A Battle Against Orcish Invaders
Factors: castle siege, orc attacks, heroism, sacrifice, leadership, magic
Setting: Gazeward Castle, an ancient fortress built into a mountain that is under attack by green-skinned orcs. The orcs are rampaging through the corridors, killing both men and women, and even children are not safe from their black orcish blades. Tyri, the king of the people, is determined to protect his kingdom and fights off multiple orcs at once. However, the orcs are afraid of their leader, Iros, who uses a magical whip to draw blood from those who flee. With Iros leading the charge, the orcs eventually overpower Tyri, behead him, and display his head on a spear shaft for all to see.
Anything else?
The story could also include elements of despair and hopelessness as the castle is being overrun. It could also highlight the bravery and selflessness of other characters who fight alongside Tyri, as well as the people who helped to defend the castle in other ways. The use of magic by Iros could add an interesting element to the story, and could be explored further in terms of how it affects the battle and the characters involved. The fall of Gazeward Castle could ultimately serve as a turning point in the larger conflict between humans and orcs.
What could the possible morales of the story be?
Well?
Possible morals of the story could include:
1. Courage and heroism in the face of overwhelming odds
2. The true meaning and cost of leadership and sacrifice
3. The danger of underestimating one's enemies
4. The destructive power of violence and warfare
5. The importance of unity and cooperation in times of crisis
6. The corrupting influence of power and magic
7. The need to find hope even in the darkest moments.
Is the story sad?
Yes, the story has sad elements such as the fall of Gazeward Castle, the death of King Tyri, and the defeat of the defenders. The story carries a sense of sorrow and despair as the orcs ruthlessly kill the people of Gazeward Castle. However, it also focuses on the bravery and heroism of Tyri, who fought until his very last breath to protect his people.
Tyri is the embodiment of glory in the story?
Yes, Tyri can be seen as the embodiment of glory in the story. Despite being outnumbered and facing a much stronger enemy, he still chose to fight and protect his people till the very end. He fought off multiple orcs at once and was only defeated when he faced Iros, the orc leader with magic. Even then, he continued to fight until his last breath. His brave actions inspired the people of the castle to fight alongside him, and his death marked a significant turning point in the story. Through his heroism and sacrifice, he has become a symbol of glory for the people of the castle to remember.
Can you tell me the factors, setting, morales, and a possible title for this story:
"Seven men have fallen to the archers of cool," Gaf spoke blood gushing from his temple, "It is lost."
"No," Ganla spoke in comforting tones, "We will fight, or die with honor."
"But I fear death," Gaf said as he leaped up and the fear could be seen in his dark eyes, "I do not desire to die!"
"Has any human ever desired that? I mean, truly desired that?" Ganla retorted sadly.
Factors: warriors, archers, battle, fear of death, honor, heroism, defeat
Setting: It is unclear from the passage what the setting is or where the battle is taking place, but it seems to be a war-torn and dangerous location.
Morals:
1. The fear of death is a natural human emotion and is nothing to be ashamed of.
2. True heroism involves facing one's fears and fighting for what is right, even when the odds are against you.
3. The pursuit of honor can provide a sense of purpose and motivation during difficult, life-threatening situations.
4. The cost and sacrifice of war, including the tragic loss of life, can have a heavy toll on those left behind.
Possible Title: Bloodshed and Sacrifice: A Tale of Warriors and Archers
And what about this one:
"I would pull out every lying tongue if I were a young man again," Vog spoke with disgust, "I hate filthy liars, they deserve to die in a fire, and then feel my ire, till they at last expire," he spoke in a rhyme.
"It is true milord," Barrca said with a slight nod, "Liars are indeed a wicked sect, they should be outrooted from all of Hanlaria," he shouted loudly his voice echoing in the dark cave.
Vog coughed, "My old lungs are not made for this place of dust and rock, I will die," he spoke slowly and Barrca rushed to his side, "Avenge me, we were trapped by that wicked elf Corco, avenge me."
"No," Barrca spoke in despair, "Do not die upon me, not when I need you! Corco will be punished, but do not die!"
Vog's eyes glazed over, he sighed his final sigh and Barrca buried his face into the old man's shirt. First sorrow filled him, and then hate, he would escape the trapped cave, he would kill Corco and all the people associated with him."
Factors: lying, hate, revenge, death, betrayal, escape, justice
Setting: The story takes place in a dark cave where Vog and Barrca are trapped by their enemy, Corco.
Morals:
1. Hatred and revenge can cloud a person's judgment and lead them to make irrational decisions.
2. The consequences of one's actions can have profound effects on those around them, even after they have died.
3. Betrayal and deception can have severe consequences for both the perpetrator and the victim.
4. Seeking justice for wrongs committed is important, but it should not consume a person's life or lead them to become blinded by hate.
Possible Title: The Consequences of Deception: A Tale of Betrayal and Revenge
And?
Another possible title for this story could be "Blinded by Hate: A Tale of Vengeance and Tragedy." This title emphasizes how the character Barrca is consumed by his desire for revenge and how it ultimately leads to tragedy. The story also highlights the importance of empathy and understanding, as characters like Vog express their hatred towards liars without considering their motivations or circumstances. The ultimate fate of the characters involved also suggests that the cycle of violence and retribution perpetuated by Barrca and others is ultimately futile and self-destructive.
What do you think happens at the end of the book?
Based on the given passage, it's unclear how the story concludes beyond the death of Vog and Barrca's resolve to seek revenge against Corco and his associates. However, it's possible that the story could explore the themes of vengeance and justice further, showing the potential consequences of Barrca's actions and how his desire for revenge may lead him down a dark path. It's also possible that the story could introduce additional characters, conflicts, and plot twists that give the story a more complex and nuanced resolution.
Now I want you to write a short story with two characters, Nal, and Porl, Nal is fast. Porl is strong. Write a short fight scene between them in the woods, and include a little dialogue about the lines of revenge and justice.
Do it please.
Let the first term be x.
The second term is xr, where r is the common ratio.
The third term is xr^2.
The fourth term is xr^3.
Given that the fourth term is greater than the second term by 168, we have:
xr^3 - xr = 168
r^2 = 168/x
The difference between the third and first terms is xr^2 - x = 42
xr^2 - x = 42
x(r^2 - 1) = 42
x = 42/(r^2 - 1)
Substituting the value of r^2 from the first equation, we have:
x = 42/(168/x - 1)
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0
x = -7 or 6
Since the first term of a geometric progression cannot be negative, the first term is 6.