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

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Oct 23, 2016


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:


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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