what is the common difference in the following arithmetic sequence?\n$\frac{2}{3},\frac{1}{6},-\frac{1}{3},-\…

what is the common difference in the following arithmetic sequence?\n$\frac{2}{3},\frac{1}{6},-\frac{1}{3},-\frac{5}{6},cdots$\n-4\n$-\frac{1}{2}$\n$\frac{1}{9}$\n4

what is the common difference in the following arithmetic sequence?\n$\frac{2}{3},\frac{1}{6},-\frac{1}{3},-\frac{5}{6},cdots$\n-4\n$-\frac{1}{2}$\n$\frac{1}{9}$\n4

Answer

Explanation:

Step1: Recall common - difference formula

The common difference $d$ of an arithmetic sequence is $d=a_{n + 1}-a_{n}$. Let $a_{1}=\frac{2}{3}$ and $a_{2}=\frac{1}{6}$.

Step2: Calculate the common difference

$d=\frac{1}{6}-\frac{2}{3}=\frac{1 - 4}{6}=-\frac{3}{6}=-\frac{1}{2}$

Answer:

$-\frac{1}{2}$