Given first term a = 20

Second term t_{1} = 22

Third term t_{2} = 24

Common difference d = t_{2} – t_{1} = 24 – 22 = 2

We need to find t_{15} 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.

⇒ t_{15} = 20 + (15 – 1) × 2

⇒ t_{15} = 20 + 14 × 2

⇒ t_{15} = 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. S_{27}

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,

⇒S_{27} = 27 × 46

⇒S_{27} = 1242