Answer:
a) Sum = 28n + n² + n
b) 492 seats
c) 3950 seats
Step-by-step explanation:
The given data forms arithmetic series.
30, 32, 34,.........
Total rows = n = 50.
a = first term = 30
Common difference = d = second term - first term
= 32 -30
= 2
a) Sum = (28 + 2) + (28 + 4) +.................+ 28 + 2n
= 28n + (2 + 4 + ...... +2n)
Sum of first 'n' even numbers = n*(n+1)
= 28n + n *(n + 1)
= 28n + n² + n
b) To find the number seats in the first 12 rows, use the formula,
[tex]\boxed{\bf S_n =28n +n^2 + n}[/tex]
[tex]\sf S_{12} = 28*12 +12^2 + 12\\\\[/tex]
= 336 + 144 + 12
= 492
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c)
[tex]\sf S_{50} =28*50 + 50^2 + 50\\\\[/tex]
= 1400 + 2500 +50
=3950
Total seat available in the whole amphitheatre = 3950 seats
