Question

The first and the last term of an ap are 5 and 45 respectivelyif the sum of all its terms is 400, find its common difference ​

Answer 1

Sn =n/2(a +l)

400=n/2(5+45)

400=n/2(50)

400=25n

N=16

Tn =a+(n-1)d

45=5+(16-1)d

40=15d

D=8/3

Answer 2

a = 5

an = 45

a + (n-1)×d = 45

5 + (n-1)d = 45

(n-1)d = 40 ...(i)

Sn = 400

n/2 (2a + (n-1)d) = 400

n (2×5 + 40) = 400 × 2

n (10 + 40) = 800

n (50) = 800

n = 800/50

n = 16

Put n = 16 in eq. ...(i)

(n-1)d = 40

(16-1)d = 40

15d = 40

d = 40/15

d = 8/3