Question

I got n= 8/5, -1, but I don't think it's right. I would really appreciate any help with this :)

Answer 1

S₈ = 296

Explanation:

Given: 2 + 12 + 22 + 32 + .... + (10n - 8) =
`$5n^2 - 3n $`

To prove
`$ S_8 $` is true, substitute
`$ n = 8 $` and compare LHS and RHS

n = 8:

`10n - 8 = 10(8) - 8`

`$ \implies 72 $`

`$ \therefore LHS = 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 $`

`$ = 296 $`

Now, Substituting n = 8 in RHS, we get:

`$ 5n^2 - 3n = 5(8)^2 - 3(8) = 5(64) - 24 $`

`$ = 296 $`

Therefore, RHS = 296

We see, LHS = RHS

Hence, we can conclude that
`$ S_8 $` is correct.