I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given. Please help!

Also, a similar question dealing with the same kind of problem is this: The sum of the first 12 terms in an arithmetic sequence is 156. What is the sum of the first and twelfth terms? Here I tried using the formula: Sn = n/2 [2a + (n-1)d] (where n is the number of terms, a is the first term, and d is again the common difference). I have two unknowns and I don't know how to find even one!! Help!

Thanks! Rachel

Hi Rachel,

For the first problem I used the same procedure as you did.

1/2 = a + 4d

7/8 = a + 19d
Subtracting the first equation from the second gives 3/8 = 15 d and hence d = 3/120 = 1/40 I then substituted this value of d into 1/2 = a + 4d to get a = 1/2 - 1/10 = 2/5

For the second problem, when n = 12,

156 = 6(2a + 11d). The first term is a and the twelfth term is a + 11d so the sum of the first and twelfth terms is 2a + 11d This is actually how I remember the expression for the sum of an arithmetic sequences. It is (the first term + the last term) times (the number of terms)/2

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