Algebra

Firstly, this is not really the sum of 1 sequence, it is the sum of 2 sequences

\(1^2+3^2+5^2+ .......\\ 2.5^2+2.7^2+2.9^2......\\ S_{20}=1^2+3^2+5^2+ .......+19^2\quad+ \quad 2.5^2+2.7^2+2.9^2......+4.3^2\)

I suppose I could just calculate the answer.

\(S_{20}=1330+118.9 = 1448.9\\ A=1448.9/20=72.445\)

Doesn't look like any of those answers to me.

Another way is to notice that every term in the series is less than 20^2. Since there are 20 terms in all we must have S20 < 20*20^2, which means that 20A < 20*20^2, or A < 20^2  or A < 400.  Hence e) is the answer.