Question

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

Answer 1

See explanation.

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