Question

15. A conference hall has 33 rows of seats. The last row contains 80 seats.
If each row has two fewer seats than the row behind it, how many seats
are there in the first row?
a. 14
b. 16
c.18
d.20​

Answer 1

The following problem using arithmetic progression as same number of seats are being reduced. So, We have

• Common difference, d = 2
• First term, a = ?
• Last term, l = 80
• Number of terms, n = 33

We have to find the value of a i.e., number of seats in the first row.

'a' can be calculated using the nth-term formula, where the nth term is l = 80,

⇒ aₙ = a + (n - 1)d

⇒ a₃₃ = a + (33 - 1)2

⇒ 80 = a + 32×2

⇒ 80 = a + 64

⇒ a = 80 - 64

⇒ a = 16

So, The value of a is 16.

Hence, There are 16 seats in the first row.

∴ Option (b) is correct.

Answer 2

Answer:

a. 14

Step-by-step explanation:

2×32 = 64

80-64 =14