Answer:
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]
The number of chairs in the concert hall is 588.
Number of chairs in the first row = 16
Number of chairs in the second row = 16 + 4 = 20
Number of chairs in the third row = 20 + 4 = 24
Number of chairs in the fourth row = 24 + 4 = 28
Number of chairs in the fifth row chairs = 28 + 4 = 32
Number of chairs in the sixth row = 32 + 4 = 36
Number of chairs in the seventh row = 36 + 4 = 40
Number of chairs in the eighth row = 40 + 4 = 44
Number of chairs in the ninth row = 44 + 4 = 48
Number of chairs in the tenth row = 48 + 4 = 52
Number of chairs in the eleventh row = 52 + 4 = 56
Number of chairs in the twelfth row = 56 + 4 = 60
Number of chairs in the thirteenth row = 60 + 4 = 64
Number of chairs in the fourteenth row = 64 + 4 = 68
Total number of chairs is the sum of all the chairs in the rows = 588
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