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

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Answer 1 · 2016-10-23T09:38:53

See explanation.

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:

${(a_1+d=4),(a_1+4d=10):}$

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