Question

An arithmetic has 3 as it first term also the sum of the first 8 term is twice the sum of the 5 term. Find the common different?

Answer 1

`d = 3/4`

Explanation:

We must write an equation using the formula `s_n = n/2(2a + (n - 1)d)`, in order to solve for `d`, the common difference.

We know that `s_8 = 2(s_5)`, and that `a = 3`, so our equation will be:

`8/2(2(3) + (8 - 1)d) = 2(5/2(2(3) + (5- 1)d))`

`4(6 + 7d) = 5(6 + 4d)`

`24 + 28d = 30 + 20d`

`24 - 30 = 20d - 28d`

`-6 = -8d`

`d = 3/4`

If you recheck using the formula `s_n = n/2(2a + (n - 1)d)`, you will find that `s_5 = 45/2` and `s_8 = 45`, which makes our answer correct (since `2s_5 = s_8`).

Hopefully this helps!