Use
S=n2 to find the sum of 1+3+5+. . . + 301.

I'm not sure what the question means by "use S = n^2"...

At any rate, the given sum

1 + 3 + 5 + … + 301

is simply the sum of the first 151 odd positive integers, which we can write in the form 2n - 1 for n between 1 and 151. That is,

We can expand the sum as

Next, recalling that

it follows that

(Probably "S = n^2" means "sum of n odd integers = n ²")