Question 119

# A multi-storied office building has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row, there are 2 more parking spaces than in the previous row. The total number of parking spaces in the office building is

Solution

$$R_{1}$$= 20 , $$R_{2}$$= 21 , $$R_{3}$$= 23 ...

Sum = 20+$$\underbrace{21+23+...upto 16 terms}$$

So apart from first term the above mentioned sum represents an Arithmetic Progression that has 16 terms.

Sum of A.P. = $$\frac{16}{2}[2(21)+(16-1)2]$$  = 576

So total number of parking spaces = 20+576 = 596