3. The first row of seats in a theater has 15 seats and each successive row has 3 more seats than the row before it. If the theater has 12 rows of seats, how many seats are there in all?
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20 rows
Explanation:
Write a formula to illustrate this arithmetic sequence:
a
n
=
15
+
3
(
n
−
1
)
Using the sum formula:
870
=
n
2
(
15
+
15
+
3
(
n
−
1
)
)
1740
=
3
n
2
+
27
n
1740
=
3
(
n
2
+
9
n
)
580
=
n
2
+
9
n
n
2
+
9
n
−
580
=
0
(
n
+
29
)
(
n
−
20
)
=
0
n
=
20