the first term of A.P is 5 and the last term is 45 and the sum of all term is 400. find the number of terms and the Common difference.
help me plz ​

Answer:

[tex]n =16[/tex] --- Number of terms

[tex]d = \frac{8}{3}[/tex] --- Common difference

Explanation:

Given

[tex]a = 5[/tex] --- first term

[tex]T_n = 45[/tex]

[tex]S_n = 400[/tex]

Required

Determine the number of terms (n) and the common difference (d)

The sum of n terms of an AP is:

[tex]S_n = \frac{n}{2}(a + T_n)[/tex]

This gives:

[tex]400 = \frac{n}{2}(5 + 45)[/tex]

[tex]400 = \frac{n}{2} * 50[/tex]

[tex]400 = n * 25[/tex]

Divide both sides by 25

[tex]16 = n[/tex]

[tex]n =16[/tex]

The nth term of an AP is:

[tex]T_n = a + (n - 1)d[/tex]

This gives:

[tex]45 = 5 + (16 - 1) * d[/tex]

[tex]45 = 5 + 15 * d[/tex]

Subtract 5 from both sides

[tex]45 - 5= 5 - 5 + 15 * d[/tex]

[tex]40= 15 * d[/tex]

Divide both sides by 15

[tex]\frac{40}{15} = d[/tex]

[tex]\frac{8}{3} = d[/tex]

[tex]d = \frac{8}{3}[/tex]

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Marks: 1
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(b)
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(C
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(d)
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Metaphors Worksheet (Meanings Part 2)
[Animated image]
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Read the excerpt from Chapter 4.
Anne of Green Gables

by Lucy Maud Montgomery

Matthew Cuthbert and his sister Marilla had decided to adopt a boy to help on their farm called Green Gables. When a girl, Anne, arrives, they are surprised. In this excerpt, Anne has just awoken after her first night at Green Gables.

Anne could evidently be smart to some purpose for she was down-stairs in ten minutes’ time, with her clothes neatly on, her hair brushed and braided, her face washed, and a comfortable consciousness pervading her soul that she had fulfilled all Marilla’s requirements. As a matter of fact, however, she had forgotten to turn back the bedclothes.

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“For pity’s sake hold your tongue,” said Marilla. “You talk entirely too much for a little girl.”

Thereupon Anne held her tongue so obediently and thoroughly that her continued silence made Marilla rather nervous, as if in the presence of something not exactly natural. Matthew also held his tongue,—but this was natural,—so that the meal was a very silent one.

As it progressed Anne became more and more abstracted, eating mechanically, with her big eyes fixed unswervingly and unseeingly on the sky outside the window. This made Marilla more nervous than ever; she had an uncomfortable feeling that while this odd child’s body might be there at the table her spirit was far away in some remote airy cloudland, borne aloft on the wings of imagination. Who would want such a child about the place?

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Question 1
Part A

What is a theme of Anne of Green Gables?


Some people can find ways to stay positive under any circumstances.

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It's difficult to imagine possibilities when life has been hard.

Children should be given the opportunity to express themselves.
Question 2
Part B

Which detail from the story best supports the answer to Part A?


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“Yet Matthew wished to keep her, of all unaccountable things!”

“‘But I'm glad it’s not rainy today because it’s easier to be cheerful and bear up under affliction on a sunshiny day.’”

“Who would want such a child about the place?”



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plz help for these questions..I wil surely mark u as brainlist and 50 points​

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