Question

A theater owner wants to provide enough seating for 957 people. The main floor has 27 rows of 26 seats in each row. If the balcony has 17 rows, how many seats must

be in each row to satisfy the owner's seating requirements?
There must be seats in each balcony row.

Answer 1

SOLUTION:-

No. of logs in bottom row =20No. of logs in next row =19No. of logs in next row to it =18Hence the AP series is 20,19,18.......Where first term (a)=20and common difference (d)=−1∴Sn=2n[2a+(n−1)d] Let n rows are required to the 200 logs]∴2n[2a+(n−1)d]=200⇒2n[2×20+(n−1)(−1)]=200⇒40n=n2+n=400⇒n2−4n+400=0⇒n2−25n−16n+400=0⇒n(n−25)−16(n−25)=0⇒(n−16)(n−25)=0∴n=16,25As 25 rows are not popssible ∴ No. of rows required =16And , no. of logs placed in top (16th) row =5