A Recursion Formula and the Initial Term(s) of a Sequence $$a _ { 1 } = 1 , a _ { n + 1 } = \frac { n a _ { n } } { n + 5 }$$

question 12

Multiple Choice

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.
- $$a _ { 1 } = 1 , a _ { n + 1 } = \frac { n a _ { n } } { n + 5 }$$

• A) \(1 , \frac { 1 } { 6 } , \frac { 2 } { 42 } , \frac { 6 } { 336 } , \frac { 24 } { 3024 }\)
• B) \(1 , \frac { 1 } { 6 } , \frac { 2 } { 42 } , \frac { 3 } { 336 } , \frac { 4 } { 3024 }\)
• C) \(1 , \frac { 1 } { 6 } , \frac { 7 } { 6 } , \frac { 7 } { 48 } , \frac { 63 } { 480 }\)
• D) \(1 , \frac { 1 } { 6 } , \frac { 2 } { 7 } , \frac { 6 } { 8 } , \frac { 24 } { 9 }\)

---

Definitions:

Conscientiousness

One of the Big Five personality traits, describing individuals who are organized, dependable, and disciplined.

Messy

Describes a state of disorder, disarray, or confusion, often implying a lack of organization.

Agreeableness

A personality trait characterized by warmth, kindness, and a cooperative disposition.

Combative

Displaying readiness or eagerness to fight or argue; aggressively confrontational.