How do you tell whether the sequence 1, 1 1/6, 1 1/3, 1 1/2 is arithmetic and if it is, what is the common difference?

Jun 19, 2018

color(blue)("Hence it's an Arithmetic Sequence with c.d. = " d = 1/6

Explanation:

$a = 1 , {a}_{2} = 1 \left(\frac{1}{6}\right) , {a}_{3} = 1 \left(\frac{1}{3}\right) , {a}_{4} = 1 \left(\frac{1}{2}\right) , . . .$

$\text{Common Difference } d = {a}_{2} - a = 1 \left(\frac{1}{6}\right) - 1 = \left(\frac{1}{6}\right)$

$d = {a}_{3} - {a}_{2} = 1 \left(\frac{1}{3}\right) - 1 \left(\frac{1}{6}\right) = \frac{1}{6}$

$d = {a}_{4} - {a}_{3} = 1 \left(\frac{1}{2}\right) - 1 \left(\frac{1}{3}\right) = \frac{1}{6}$

color(blue)("Hence it's an Arithmetic Sequence with c.d. = " d = 1/6