Sequences and Series: Arithmetic Sequences

arithmetic sequence  An arithmetic sequence is a list of numbers in which consecutive terms differ by a constant amount, the common difference When the common The nth or general term of an arithmetic sequence is given by an=a1+d So in our example a1=2 and d=4 so an=2+4=2+4n−4=4n−2

In y = ax +b when are a, -ba, b in arithmetic progression The polynomial y = ax^2 + bx + c has roots r1 and r2 Can a, r1, b, r2 and c be in arithmetic Explanation This formula tells us that, guven an arithmetic sequence, we can find the common difference d by subtracting any term from the next For example,

If the first term of the sequence is a and the common difference is d, then the arithmetic sequence can be written as a, a+d, a+2d, a+3d, …, a+d, … Finding the number of terms in an arithmetic sequence might sound like a complex task, but it's actually pretty straightforward