Find a formula for the nth term of the sequence.
-$0,0,2,2,0,0,2,2$ (alternating 0's and 2's in pairs)
A) $a _ { n } = 1 + ( - 1 ) ^ { n ( n + 1 ) }$
B) $a _ { n } = 1 - ( - 1 ) ^ { n ( n - 1 ) }$
C) $\mathrm { a } _ { \mathrm { n } } = 1 + ( - 1 ) ^ { \mathrm { n } ( \mathrm { n } + 1 ) / 2 }$
D) $a _ { n } = 1 + ( - 1 ) ^ { n ( n - 1 ) }$

Question

Quizplus · Accepted Answer

The sequence alternates between 0's and 2's every two terms, so we can split the sequence into two: $0,0,0,0,\ldots$ and $2,2,2,2,\ldots$. The first sequence is just all 0's, so we can ignore it. The second sequence is defined by $a_n = 2$ if $n$ is odd and $a_n = 0$ if $n$ is even. This is equivalent to $a_n = 1 + (-1)^{\frac{n(n+1)}{2}}$, which matches choice C.

Find a Formula for the Nth Term of the Sequence 0,0,2,2,0,0,2,20,0,2,2,0,0,2,20,0,2,2,0,0,2,2

Find a Formula for the Nth Term of the Sequence $0,0,2,2,0,0,2,2$