Use Picking Numbers
If n = 2, sum of the first 2 positive integers is (1 + 2) = 3. x = 3.
Sum of first 2n = 2(2) = 4 even integers is (2 + 4 + 6 + 8) = 20.
Plug in n=2, x=3 to answer choices to find the answer that is = 20.



(a): $2x + 2n^{2}$ = 2(3) + 2(2$^{2}$) = 6 + 2(4) = 6 + 8 = 14. Eliminate.
(b): $3x + 4n^{2}$ = 3(3) + 4(2$^{2}$) = 9 + 4(4) = 9 + 16 = 25. Eliminate.
(c): $4x + n^{2}$ = 4(3) + 2$^{2}$ = 12 + 4 = 16. Eliminate.
(d): $4x + 2n^{2}$ = 4(3) + 2(2$^{2}$) = 12 + 2(4) = (12 + 8) = 20 (= Answer)