The ninth and tenth terms of an arithmetic sequence are 1/4 and -1/3, respectively. What is the second term?
The ninth and tenth terms of an arithmetic sequence are 1/4 and -1/3, respectively. What is the second term?
Let's use a common denominator so all we have to worry about are the top numbers.
Try 12 as the common denominator, which would be 3/12 and –4/12
So it looks like the change from any term to the next term is –7/12.
Let's work backwards, 10th term, 9th term, and keep adding 7/12 (since we're going backwards)
10 - –4/12 add 7/12 to this to get the 9th term
9 - 3/12 add 7/12 to this to get the 8th term
8 - 10/12
7 - 17/12
6 - 24/12
5 - 31/12
4 - 38/12
3 - 45/12
2 - 52/12 unless I've bungled terribly, 52/12 is the 2nd term, or 44/12 which reduces to 41/3
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