# A review center opened with only 10 students enrolling on the first month.However it has been observed that the number of students doubled every month, how many were enrolled in the 8th month ?

Jul 17, 2018

Step by step solution

#### Explanation:

1st month $10$ students
2nd month (twice greater) $20$ students
3rd month $40$ students
4th month $80$ students
5th month $160$ students
6th month $320$ students
7th month $640$ students
8th month $1280$ students.

Jul 18, 2018

$1280$ students in the $8 t h$ month

#### Explanation:

This represents a geometric sequence because each month the number of students doubles to get the number the next month,

The sequence starts: $10 , 20 , 40 \ldots . .$

${T}_{n} = a {r}^{n - 1}$ is the general term for a geometric sequence. In this case we have:

$a = 10 \text{ }$(the first term)

$r = 2 \text{ }$( the common ratio)

$n = 8 \text{ }$(we need the $8 t h$ term)

${T}_{8} = 10 {\left(2\right)}^{7} \text{ } \leftarrow 8 - 1 = 7$

${T}_{8} = 10 \times 128$

${T}_{8} = 1280$ students

Check by writing $8$ terms

$10 , 20 , 40 , 80 , 160 , 320 , 640 , 1280$