There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the 15th row and also find how many total seats are there in the auditorium?

Given first term a = 20
Second term t₁ = 22
Third term t₂ = 24
Common difference d = t₂ – t₁ = 24 – 22 = 2
We need to find t₁₅ thus n = 15
Now, by using n^th term of an A.P. formula
t_n = a + (n – 1) d
where n = number of terms
a = first term
d = common difference
t_n = n^th terms
On substituting all value in n^th term of an A.P.
⇒ t₁₅ = 20 + (15 – 1) × 2
⇒ t₁₅ = 20 + 14 × 2
⇒ t₁₅ = 20 + 28 = 48
We have been given that, there are 27 rows in an auditorium
Thus, we need to find total seats in auditorium i.e. S₂₇
Now, by using sum of n^th term of an A.P. we will find its sum

Where, n = number of terms
a = first term
d = common difference
S_n = sum of n terms
Thus, on substituting the given value in formula we get,

⇒S₂₇ = 27 × 46
⇒S₂₇ = 1242