# Thread: Help with question in Arithmetic sequences. AS level homeschooling

1. ## Help with question in Arithmetic sequences. AS level homeschooling

I'm going through some past exams and I came upon a question that I have absolutely no idea how to even start. I found the answer in a mark scheme but I have no idea how to get to it nor do I understand the working. It's probably something very simple but for some reason I have hit a blank.

Question:
An arithmetic progression has first term a and common difference d. It is given that the
sum of the first 200 terms is 4 times the sum of the first 100 terms.

a. Find d in terms of a.
b. Find the 100th term in terms of a.

Answer in mark scheme:
(i) 200/2(2a + 199d)
= 4 × 100/2(2a + 99d)d = 2a

(ii) a + 99d
= a + 99 × 2a
199a

An help with this would be deeply apreciated. Thank you in advance

2. Originally Posted by Sithranio
I'm going through some past exams and I came upon a question that I have absolutely no idea how to even start. I found the answer in a mark scheme but I have no idea how to get to it nor do I understand the working. It's probably something very simple but for some reason I have hit a blank.

Question:
An arithmetic progression has first term a and common difference d. It is given that the
sum of the first 200 terms is 4 times the sum of the first 100 terms.

a. Find d in terms of a.
b. Find the 100th term in terms of a.

Answer in mark scheme:
(i) 200/2(2a + 199d)
= 4 × 100/2(2a + 99d)d = 2a

(ii) a + 99d
= a + 99 × 2a
199a

An help with this would be deeply apreciated. Thank you in advance
They are using formulas you should have learned, for the nth term of an arithmetic sequence, and for the sum of the first n terms.

Have you learned any such formulas? Please show what you have learned, so we can start there in explaining it.

3. Originally Posted by Sithranio
I'm going through some past exams and I came upon a question that I have absolutely no idea how to even start. I found the answer in a mark scheme but I have no idea how to get to it nor do I understand the working. It's probably something very simple but for some reason I have hit a blank.

Question: An arithmetic progression has first term a and common difference d. It is given that the sum of the first 200 terms is 4 times the sum of the first 100 terms.

a. Find d in terms of a.
b. Find the 100th term in terms of a.
To learn about arithmetic sums and sequences, please try here. Please study at least two lessons from the listing. Then please attempt the exercise.

If you get stuck, please reply showing your thoughts and efforts so far. Thank you!

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