Write a formula for the general term, or nth term, for the given sequence.
-$$1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots$$
A) $a _ { n } = \frac { 2 n } { ( n + 1 ) ! }$
B) $a _ { n } = \frac { 2 ^ { n + 1 } } { n ! }$
C) $a _ { n } = \frac { 2 ^ { n } } { n ! }$
D) $a _ { n } = \frac { 2 ^ { n } } { ( n + 1 ) ! }$

Question

Quizplus · Accepted Answer

The pattern of the sequence can be observed by looking at the numerator and the denominator separately. The numerator follows a pattern of being 2 raised to the power of n, where n starts from 1. The denominator is the factorial of (n+1), where n also starts from 1. Therefore, the general term for the nth term of the sequence is $a_n = \frac{2^n}{(n+1)!}$.

Write a Formula for the General Term, or Nth Term 1,23,13,215,…1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots1,32​,31​,152​,…

Write a Formula for the General Term, or Nth Term $1 , \frac { 2 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 15 } , \ldots$