The first term of an AP is 5 and the last term is 45. If the sum of all the terms

Question

The first term of an AP is 5 and the last term is 45. If the sum of all the terms is 400, the number of terms is:

Smart Achievers · Accepted Answer

(4)

$W e h a v e a = 5, a ₙ = 45 = l a n d S ₙ = 400 ∴ S_{n} = n / 2 (a + l) \Rightarrow 400 = n / 2 (5 + 45) \Rightarrow 400 = n / 2 \times 50 \Rightarrow 25 n = 400 ∴ n = 400 / 25 \Rightarrow n = 16$

Solution

Q.
The first term of an AP is 5 and the last term is 45. If the sum of all the terms is 400, the number of terms is:

1 20

2 8

3 10

4 16

Ans.
(4)

$W e h a v e a = 5, a ₙ = 45 = l a n d S ₙ = 400 ∴ S_{n} = n / 2 (a + l) \Rightarrow 400 = n / 2 (5 + 45) \Rightarrow 400 = n / 2 \times 50 \Rightarrow 25 n = 400 ∴ n = 400 / 25 \Rightarrow n = 16$

Want Us to Email you About Special Offers & Updates?