Question

The common difference of the arithmetic sequence 1/2, 5/6, 7/6, 3/2, 11/6

Answer 1

Answer:

$\boxed{\dfrac{1}{3}}$

Step-by-step explanation:

You have an arithmetic sequence in which the terms are

½, ⅚, ⁷/₆, ³/₂, ¹¹/₆

1. Give all the fractions a common denominator

Your sequence looks like this:

³/₆, ⅚, ⁷/₆, ⁹/₆, ¹¹/₆

2. Calculate the difference

The common difference is the difference between consecutive terms.

$\begin{array}{rcccl}a_{2} - a_{1} & = & \dfrac{5}{6}-\dfrac{3}{6} & = & \dfrac{2}{6} = \dfrac{1}{3}\\\\a_{3} - a_{2} & = & \dfrac{7}{6}-\dfrac{5}{6} & = & \dfrac{2}{6} = \dfrac{1}{3}\\\\a_{4} - a_{3} & = & \dfrac{9}{6}-\dfrac{7}{6} & = & \dfrac{2}{6} = \dfrac{1}{3}\\\\a_{5} - a_{4} & = & \dfrac{11}{6}-\dfrac{9}{6} & = & \dfrac{2}{6} = \dfrac{1}{3}\\\\\end{array}\\\\\text{The common difference is }\boxed{\mathbf{\dfrac{1}{3}}}$

Answer 2

We are required to find the common difference of the arithmetic sequence 1/2, 5/6, 7/6, 3/2, 11/6

The common difference of the arithmetic sequence 1/2, 5/6, 7/6, 3/2, 11/6 is 1/3.

Given:

1/2, 5/6, 7/6, 3/2, 11/6

common difference of an A.P, d = difference between first term and second term

first term = 1/2

second term = 5/6

d = 5/6 - 1/2

= (5 - 3) / 6

= 2/6

divide through by 2

d = 1/3

Therefore, the common difference of the arithmetic sequence 1/2, 5/6, 7/6, 3/2, 11/6 is 1/3.

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