Question

Find the nth term of the sequence

-3, 0, 5, 12

Work out the reciprocal of 2 x 10(9,as a power). Give your answer in standard form.

Answer 1

Hello,


Adding 4 to each term we find 1,4,9,16,....

`u_1=-3\\ u_2=0\\ u_3=5\\ u_4=12\\ Let's\ assume\ v_n=u_n+4\\ v_1=-3+4=1=1^2\\ v_2=0+4=4=2^2\\ v_3=5+4=9=3^2\\ v_4=12+4=16=4^2\\ ...\\ v_n=n^2\\ u_n=v_n-4\\\\ \boxed{u_n=n^2-4}`