Given a sequence 0,43,163,649,..., then the 12th term of this sequence is....
Explanation
Given sequence
0,43,163,649,...
Each term if expanded becomes
u1=0=201−201=21−11+(−1)1⋅22(1−1)1
u2=43=211+221=22−11+(−1)2⋅22(2−1)1
u3=163=221−241=23−11+(−1)3⋅22(3−1)1
u4=649=231+261=24−11+(−1)4⋅22(4−1)1
Therefore, the nth term can be formulated as follows
un=2n−11+(−1)n⋅22(n−1)1
Then the 12th term is
u12=212−11+(−1)12⋅22(12−1)1
u12=2111+1(22(11)1)
u12=2111+2221