How do I find the first term of an arithmetic sequence?

Kolby Castillo 2022-09-17 Answered
How do I find the first term of an arithmetic sequence?
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Answers (1)

brodireo1
Answered 2022-09-18 Author has 12 answers
To answer this (or any other) question I need some data. It is impossible to solve such task without having anything given.
If I had two terms I could use the n−th term formula to calculate the first term.
For example:
The second term of an arithmetic sequence is 4. The fifth is 10. Find the first term.
In this task we have 2 terms given: a 2 = 4 and a 5 = 10 . We can use the n−th term formula to build a system of equations:
{ a 1 + d = 4 a 1 + 4 d = 10
If we subtract the first equation from the second we can calculate d:
3d=6; d=2
Now if we substitute the calculated value we see that: a 1 + 2 = 4 , so a 1 = 2 .
Now we can answer that The first term of this sequence is 2

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