Question

4. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number
of terms and the common difference.
[NCERT​

Answer 1

Answer:

Number of terms = 16, Common difference = 8/3

Step-by-step explanation:

Given :

First term of an AP ( a ) = 5

Last term of an AP ( l ) = 45

Sum of first n terms of AP ( Sₙ ) = 400

Using Sum of n terms of an AP formula

Sₙ = n/2 × ( a + l )

⇒ 400 = n/2 × ( 5 + 45 )

⇒ 800 = 50n

⇒ 800/50 = n

⇒ n = 16

Last term of the AP ( aₙ ) = 45

Using nth of AP formula

⇒ aₙ = a + ( n - 1 )d

⇒ 45 = 5 + ( 16 - 1 )d

⇒ 45 - 5 = 15d

⇒ 40 = 15d

⇒ 40/15 = d

⇒ d = 8/3

Therefore the number of terms of the AP is 16 and the common difference is 8/3.

Answer 2

Answer:

Step-by-step explanation:

let a be first term, l be the last term, d be the common difference and s be the sum of no's

now,

s=n/2(a+l)

400=n/2(5+45)

400=n/2(50)

2*400=50n

800=50n

800/50=n

16=n

now we know

l=a+(n-1)d

45=5+(16-1)d

45-5=(16-1)d

40=15d

d=40/15

d=8/3

hence final answer is

d=8/3

n=16

hope it helped