Question

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference

Answer 1

let a be the first term and d be the common difference

given a=3

S8=2xS5 ....(i)

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

using (i)

(8/2)(6+7d) = 2 (5/2)(6+4d)

which is a linear in d, solving this will give us our common difference d.

4*(6+7d)= 5*(6+2d)

24+28d=30+10d

18d=6

d= 6/18 = 1/3

I hope I didn't do any silly mistakes and this helps.

thanks

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Answer 2

Answer:

The first term a1, and a2=a1+d, and a3=a1+2d, and so on. In an arithmetic progression d is the common difference, and the Sum of n terms:

Sn =a1+a2+a3+...+an

Here, we have

a1=3

S8=2(S5)

a1+a2+a3+a4+a5+a6+a7+a8 = 2(a1+a2+a3+a4+a5)

As you know a2=a1+d and a3=a1+2d, and so on.

So,

8a1+28d = 2(5a1+10d)

8a1+28d=10a1+20d

8d=2a1

d=a1/4

d=3/4

So, the common difference is: d=3/4  

Step-by-step explanation: