In a concert hall, there are 16 chairs in the first row, and each row has 4 more chairs than the previous row. There are 14 rows altogether. How

many chairs are there in the concert hall?

O A. 68

O

o

B. 588

C. 616

D.

1,176

Option B 588

Step-by-step explanation:

In the first row there are 14 chairs:

r1 = 16

In the second there are 16 plus 4 extra chairs:

r2 = 16 + 4 = r1 + 4 = 20

In the third there are 20 plus 4 extra chairs:

r3 = 20 + 4 = r2 + 4 = r1 + 8 = 24

In r4:

r4 = 24 + 4 = r3 + 4 = r2 + 8 = r1 + 12 = 28

If you notice there ir a pattern, each row rn has 16. chairs plus 4 * (n-1) extra chairs.

So, if we sum them until r14 we have:

r1 + r2 + ... + r4 = 16 + [16 + 4 (1) ] + [16 + 4 (2) ] + ... + [16 + 4 (13) ]

Notice that we have 16 summed 14 times, so we can put al the 16 together:

= 16*14 + 4 (1) + 4 (2) + ... 4 (13)

Taking 4 as common factor:

= 16*14 + 4 [ 1 + 2 + 3 + ... + 13 ]

= 16*14 + 4 [91]

= 224 + 364

= 588

Option B

Obs: you can calculate the sum of 1 to 13 using the formula that counts between 1 and n and is: n (n+1) / 2 [in this case is 13*14/2 = 91]