The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-2 , 4 , 8 , 16 , 32 , ...
A) $a _ { n } = 2 + 2 ( n - 1 )$
B) $a _ { n } = 2 n - 1 + 1$
C) $a _ { n } = 2 n$
D) $a _ { n } = 2 n$.

Question

Quizplus · Accepted Answer

The sequence is a geometric progression where each term is multiplied by 2 to get the next term. The first term $a_1 = 2$, and the common ratio $r = 2$. The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$. Substituting $a_1 = 2$ and $r = 2$, we get $a_n = 2 \cdot 2^{(n-1)}$, which simplifies to $a_n = 2^n$, not directly matching any of the given options exactly as they are presented. However, the correct interpretation of the sequence's formula seems to have been intended to be option D, despite the formula being inaccurately represented in the choices provided.

The Given Pattern Continues an=2+2(n−1)a _ { n } = 2 + 2 ( n - 1 )an​=2+2(n−1)

The Given Pattern Continues $a _ { n } = 2 + 2 ( n - 1 )$