the first term of an AP is5 the last term is 45 and the sum is 400 find the number of the term and the common difference​

a = 5

l = 45

s = 400

400 = n(a + l)/2

800 = n(50)

n = 16

l = a + (n-1)d

45 = 5 + 15d

40 = 15d

d = 40/15 = 8/3

Answer:

Given: a=5, an=45, sn=400

An=a+(n-1)d

45=5+(n-1)d

(n-1)d=40

D=40/n-1..........1

Sn= n/2(2a+(n-1)d)

400=n/2(10+(n-1)(40/n-1)) [from 1]

800=n(10+40)

800=50n

80/5=n

N=16

Subs n in 1

D=40/15

D=8/3

Hope it helps u.....^_^