Q. 44.6( 41 Votes )

# 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?

Answer :

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 = no. 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 it’s sum

Where, n = no. 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

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