The most commonly used explicit of an arithmetic sequence is given as,
an = a + (n - 1) d.
Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,
First number a1 = 18
Tolerance d = 3
Now putting the values in the given formula, we will get,
an=a1+(n-1) d
=18+(n-1)3
=3n+15
20
= ∑ 3n+15
n = 1
Sn = ∑3n+15
=3∑n+15∑1
=3 n(n+1)/2+15n
Sn =3* 20(20+1)/2+15(20)
=30 (21) +300
=630+300
=930
Total Seats 930.
Now to find the number of seats on every five lines.
5 10 15 20
= ∑ 3n+15; ∑ 3n+15 ; ∑ 3n+15 ; Ticket price for each set. $55; $50; $45
= 120 * 60 + 195 * 55 + 270 * 50 + 345 * 45
= $46950
More similar problems are solved in the link below.
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