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 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 nth term of an A.P. formula

tn = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

tn = nth terms

On substituting all value in nth 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 nth term of an A.P. we will find it’s sum

Where, n = no. of terms

a = first term

d = common difference

Sn = sum of n terms

Thus, on substituting the given value in formula we get,

S27 = 27 × 46

S27 = 1242

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