Question

Find the common difference of an A.P. whose first term in 4, the last term is 49 and the sum of all its terms is 265

Answer 1

Answer:

Step-by-step explanation:

a=4

a(n)=49.........1)

S(n)=265..... . 2)

from 1

a+(n-1)d=49

4+(n-1)d=49

(n-1)d=49-4=45.......3)

From 2)

Sn=n÷2(2a+(n-1)d)

265=n÷2(2×4+(n-1)d)

Putting value: from3)

We get

265=n÷2(8+45)

265×2=n(53)

530=53n

530÷53=n

10=n...................4)

Putting value of n from 4) in3)

We get

(10-1)d=45

9d= 45

d=5

Thus common difference (d) = 5