Question

If the sum of the arithmetic series `7 + 9 + 11 + 13 + 15 + . . .` is `25,613,712`, then how many terms were added up?

Answer 1

`5058`

Explanation:

Note that the sum of the first `n` odd numbers is `n^2`

So, writing `n` for the number of terms we are looking for:

`9+25613712 = (1+3+5)+(7+9+11+...+(2(n+3)-1))`

`color(white)(9+25613712) = (n+3)^2`

So:

`n = sqrt(9+25613712)-3 =5058`