Question

their sum?
24. The first and the last terms of an AP are 5 and 45 respectively. If the
sum of all its terms is 400, find the common difference and the number
of terms.
[CBSE 2012, '14, '17]​

Answer 1

given, a=5 l=45 Sn=400

to find, number of terms(n) and difference (d)

Sn= n/2(a+l)

400=n/2(5+45)

400×2=n×50

800=n×50

800/50=n

n= 16

Answer 2

Answer:

Given a=4 , l=a+(n-1)d = 45 , Sn=400

let n be total number of terms

let d be common difference

Sn =n/2(a+l)

400=n/2(5+45)

400=n/2×50

n=400÷50×2

n=8×2

n=16

l=a+(n-1)d

45=5+(16-1)d

40=15d

d=40/15=1.666666666666....

THEREFORE, Common difference is 40/15.

and total number of terms are 16.