Write the First Five Terms of the Sequence Defined Recursively $$a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$$

question 90

Multiple Choice

Write the first five terms of the sequence defined recursively.
- $$a _ { 1 } = 20 ; a _ { n } = \frac { 1 } { 4 } a _ { n - 1 } + 3$$

• A) \(a _ { 1 } = 20 , a _ { 2 } = \frac { 23 } { 4 } , a _ { 3 } = \frac { 13 } { 8 } , a _ { 4 } = \frac { 29 } { 64 } , a _ { 5 } = \frac { 1 } { 8 }\)
• B) \(a _ { 1 } = 20 , a _ { 2 } = 23 , a _ { 3 } = 26 , a _ { 4 } = 29 , a _ { 5 } = 32\)
• C) \(a _ { 1 } = 20 , a _ { 2 } = 5 , a _ { 3 } = \frac { 5 } { 4 } , a _ { 4 } = \frac { 5 } { 16 } , a _ { 5 } = \frac { 5 } { 64 }\)
• D) \(a _ { 1 } = 20 , a _ { 2 } = 8 , a _ { 3 } = 5 , a _ { 4 } = \frac { 17 } { 4 } , a _ { 5 } = \frac { 65 } { 16 }\)

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Definitions:

Anabolism

The metabolic pathways that construct molecules from smaller units, involving energy storage.

Nucleotide

The basic building block of nucleic acids like DNA and RNA, consisting of a sugar, a phosphate group, and a nitrogenous base.

Monosaccharide

Simple sugar carbohydrate that cannot form any simpler sugar by hydrolysis.

Nitrogenous Base

A molecule found in DNA and RNA that encodes the genetic information in cells.