Question

There is an auditorium with 35 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 twenty fifth row.

Answer 1

Because there are t₁ = 20 seats in the 1^st row, t₂ = 22 seats in the 2^nd row, t₃ = 24 seats in the 3^rd row and so on, the numbers of seats in rows are in an A.P.
Here,
First term, a = t₁ = 20
Common difference, d = t₂ – t₁ = 22 – 20 = 2
Now,
To find the number of seats in the 25^th row, we need to find the 25^th term of the A.P.
We know that the n^th term of an A.P. is t_n = a + (n – 1)d.
By taking a = 20, d = 2 and n = 25, we get:
t₂₅ = 20 + (25 – 1)2
$\Rightarrow$t₂₅ = 20 + 24 × 2
$\Rightarrow$t₂₅ = 20 + 48
$\Rightarrow$t₂₅ = 68
Thus, there are 68 seats in the 25^th row.