Question

\( -\frac{5}{6},\ -\frac{1}{2},\ -\frac{1}{6},\ \frac{1}{6},\ \frac{1}{2},\ \frac{5}{6},\ \ldots \) What is the next term?

• A. \(1\frac{1}{6}\)
• B. \(1\frac{1}{3}\)
• C. \(2\frac{1}{6}\)
• D. \(1\frac{5}{6}\)

Hint:

For fractional series, convert all terms to a common denominator before checking differences.

Answer 1

The Correct Option is A

Concept: A fractional series often follows a constant difference pattern.

Step 1: Compute successive differences. \[ -\frac12-\left(-\frac56\right) = \frac13 \] \[ -\frac16-\left(-\frac12\right) = \frac13 \] \[ \frac16-\left(-\frac16\right) = \frac13 \] \[ \frac12-\frac16 = \frac13 \] \[ \frac56-\frac12 = \frac13. \] Thus every term increases by \[ \frac13. \]

Step 2: Find the next term. \[ \frac56+\frac13 = \frac56+\frac26 = \frac76. \] \[ \frac76 = 1\frac16. \] Therefore the next term is \[ \boxed{1\frac16}. \]