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]

h who knows

step-by-step explanation: