SOLUTION: Write down the first term and the common difference of the arithmetic progression whose fifth term is 52 and the difference of the 9th and 13th term is 40. I've tried and come u

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Question 1005952: Write down the first term and the common difference of the arithmetic progression whose
fifth term is 52 and the difference of the 9th and 13th term is 40.
I've tried and come up with this but I'm pretty certain it's wrong
Difference between the 13th and 9th term = (a + 12d) – (a + 8d) = 4d = α
Fifth term is a + 4d = 52
First term a = 52 – α
Common difference d = α/4
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Write down the first term and the common difference of the arithmetic progression whose
fifth term is 52 and the difference of the 9th and 13th term is 40.
I've tried and come up with this but I'm pretty certain it's wrong
Difference between the 13th and 9th term = (a + 12d) – (a + 8d) = 4d = α
Fifth term is a + 4d = 52
First term a = 52 – α
Common difference d = α/4
5th term (a%5B5%5D):   52+=+a%5B1%5D+%2B+4d -------- eq (i) - Correct

13th term (a%5B13%5D): a%5B1%5D+%2B+12d - Correct

9th term (a%5B9%5D):   a%5B1%5D+%2B+8d - Correct



Difference of the 13th and 9th terms is 40, with the larger of the 2 being the 13th term, obviously.

This produces: a%5B1%5D+%2B+12d+-+%28a%5B1%5D+%2B+8d%29+=+40

a%5B1%5D+%2B+12d+-+a%5B1%5D+-+8d+=+40

a%5B1%5D+-+a%5B1%5D+%2B+12d+-+8d+=+40

4d = 40

d, or common difference = 40%2F4, or highlight_green%2810%29



52+=+a%5B1%5D+%2B+4%2810%29 ---------- Substituting 10 for d in eq (i)

52+=+a%5B1%5D+%2B+40

52+-+40+=+a%5B1%5D

1st term, or highlight_green%28a%5B1%5D+=+12%29



Do you see your error? I sure hope so!!