In a school prayer assembly, there are 23 students in the first row, 21 in the second, 19 in the third, and so on. There are 5 students in the last row. How many rows are there in the assembly?

In a school prayer assembly, there are 23 students in the first row, 21 in the second, 19 in the third, and so on. There are 5 students in the last row. How many rows are there in the assembly? Correct Answer 10

CONCEPT : 

• The n^th term an of the AP with first term a and common difference d is given by a_n = a + (n – 1) d.
• a_n is also called the general term of the AP. If there are m terms in the AP, then a_m represents the last term which is sometimes also denoted by l.

CALCULATION:

The number of students in the 1st, 2nd, 3rd, . . ., rows are : 23, 21, 19, . . ., 5.It forms an AP as common difference is same i.e. -2.

Let the number of rows in the assembly be n.

Here a = 23, d = – 2, a_n = 5

As, a_n = a + (n – 1) d

⇒ 5 = 23 + (n – 1) × (– 2)

⇒ – 18 = (n – 1)(– 2)

On solving we get n = 10 So, there were 10 rows in the school assembly.

Hence, option (4) is the correct answer.