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I have two arithmetic sequences. The first term of the first sequence is 0. The second term of the first sequence is the first term of the first sequence plus the first term of the second sequence. Similarly, the third term of the first sequence is the second term of the first sequence plus the second term of the second sequence. If the fifth term of the second sequence is 3, what is the fifth term of the first sequence?

 Jan 14, 2019
 #1
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Here is one way:

 

1st. Seq. = 0, -1, -1, 0, 2, 5, 9, 14, 20, 27, 35, 44........etc.
2nd. Seq =-1,  0,  1, 2,  3, 4, 5, 6,  7,   8,   9,   10.........etc.
The closed form of the 1st. sequence is:
1/2{n - 4}{n - 1}
Therefore, the 5th term of the 1st sequence is:
= 2.

 Jan 14, 2019

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