Question

If the chairs in an auditorium are arranged in an arithmetic sequence 5 th row contains 31 chair and 16 th row contains 75 chairs then find the total number of chairs if there exists 20 rows

Answer 1

rows 5 and 16 are 11 rows apart.
So, 11d = 75-31 = 44
d=4
a+4d = a+16=31, so a=15

S20 = 20/2 (2*15+19*4)

Answer 2

16-5=11, 75-31=44
d=4
First term = 4d-31
= 4×4-31
= -15
Number of chairs if there exists 20 rows
=n÷2(2f+(n-1)d)
=20÷2(2×(-15)+(20-1)4)
=460