How many numbers in the sequence
-1, -5/6, -2/3, ……….. 10/3 ?

Correct option is C

1. Given:

- Sequence: $$-1, -\frac{5}{6}, -\frac{2}{3}, \dots, \frac{10}{3}$$​ .
- Task: Determine how many numbers are in this sequence.

2. Concept/Formula Used:

- This is an **arithmetic progression (AP)** where:
- First term (a) = -1 ,
- Common difference (d) = $$-\frac{5}{6} - (-1) = \frac{1}{6}$$​ ,
- Last term (l) = $$\frac{10}{3}$$​ 
- The number of terms (n) in an AP is given by:
$$n = \frac{l - a}{d} + 1$$​

3. Solution:

- Substitute the values into the formula:
$$n = \frac{\frac{10}{3} - (-1)}{\frac{1}{6}} + 1$$​
- Simplify:
$$n = \frac{\frac{10}{3} + 1}{\frac{1}{6}} + 1$$​
$$n = \frac{\frac{10}{3} + \frac{3}{3}}{\frac{1}{6}} + 1$$​
$$n = \frac{\frac{13}{3}}{\frac{1}{6}} + 1$$​
$$n = \frac{13}{3} \times 6 + 1$$​
n = 26 + 1 = 27

4. Answer:

Option C: 27 numbers