Question

hi I was wondering if anyone could help me with finding the explicit rule for -2,-8,-18,-32,-50

Answer 1

-2,-8,-18,-32,-50
Take the differences:
-8+2, -18+8, -32+18, -50+32 =
-6, -10, -14, -18
Take differences again:
-10+6, -14+10, -18+14 = -4, -4, -4 (Differences are constant the second time).

Therefore, the relationship is quadratic:
a * n^2 where n = 1, 2, 3, 4 and 5.
put n = 1, an^2 = a = -2
Therefore -2 * n^2 is the explicit rule where n = 1, 2, 3, 4 and 5.

Answer 2

\(\large -2n^2\)

Answer 3

Thank you so much really appreciate it :)