Question

Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number of students taught after 25 years can be represented using the expression . How many students has Mr. Wright taught in 25 years?

450

500

1,050

2,100

Answer 1

Answer: 450
1st yr = 18 students
25 yrs = x
Cross multiply
x = 18 × 25
x = 450

Answer 2

Mr. Wright taught 1,050 students in 25 years.

Explanation:

Given,

The number of students Mr. Wright taught = 18,

Also, every year the number of student is increased by 2,

So, in second year, the number of students = 18 + 2 = 20,

In third year = 20 + 2 = 22,

In fourth year = 22 + 2 = 24,

.............., so on,

Hence, we get an A.P. that shows the given situation,

18, 20, 22, 24, ............. till 25 years.....

First term, a = 18,

Common difference, d = 2,

And, number of terms, n = 25,

Hence, the total number of students that have been taught by him are,

`S_n=(n)/(2)[2a+(n-1)d]`

`S_(25)=(25)/(2)[36+(25-1)2]`

`=(25)/(2)[36+24* 2]`

`=(25)/(2)[36+48]`

`=(25)/(2)(84)`

`=(2100)/(2)`

`=1050`

Third option is correct.