Question

If `(3+5+7+......+n terms)/(5+8+11+.......+10 terms)` = 7, then the value of n is?

Answer 1

See below.

Explanation:

Something is lacking...

If `(3+5+7+cdots+(n " terms"))/(5+8+11+cdots+(10n " terms")) = 7`, then the value of `n` is?

`N/D = 7` where

`N = sum_(k=1)^n (2k+1) = n + 2 (n(n+1))/2`
`D = sum_(k=1)^(10n)(2+3k)=2*10 n+3 (10n(10n+1))/2` and then

`n + 2 (n(n+1))/2=7(2*10n+3 (10n(10n+1))/2)`

and after simplification

`n(243-1049n)=0` with solutions

`n = 0` or `n=-243/1049`

Now if instead the formulation were

If `(3+5+7+cdots+(n " terms"))/(5+8+11+cdots+(10 " terms")) = 7`, then the value of `n` is?

then the result could be found by solving

`n + 2 (n(n+1))/2=7(2*10+3 (10(10+1))/2)` giving

`n = {-37, 35}`