Arithmetic Sequences

[Hockeyman]

I'm learning about arithmetic sequences and i was wondering how you would define a_n. For example if a₁ = 4, and a_n = 100, and n = 25. What is a_n? Is 100 the amount of terms? Any explanation would be appreciated.

 

[pka]

The term \(\displaystyle \L
a_n = a_1 + (n - 1)d\) is the nth term in the sequence.
The \(\displaystyle \L a_1\) is the first term, in this case 4.
So we have \(\displaystyle \L
a_{25} = 4 + (25 - 1)d = 100\), solve for d.