Ten students of a class are lined up according to their heights. Height of first student is 150 cm, and every next student is 2 cm more in height. What is the total sum of heights of these ten students ?

Total number of students (n) = 10

Height of first student (a) = 150 cm

Difference between height of every next student (d) = 2 cm

Since, the height difference between every next student is equal, so it can be considered an A.P.

By formula,

Sum of A.P. (S) = $\dfrac{n}{2}[2a + (n - 1)d]$

Substituting values we get :

$S = \dfrac{10}{2} \times [2 \times 150 + (10 - 1) \times 2] \\[1em] = 5 \times [300 + 9 \times 2] \\[1em] = 5 \times [300 + 18] \\[1em] = 5 \times 318 \\[1em] = 1590 \text{ cm}.$

Hence, the total sum of heights of ten students = 1590 cm.