Bode's Sequence, Defined By $a _ { 1 } = 0.4 , a _ { k } = 0.1 \left( 3 \cdot 2 ^ { k - 2 } + 4 \right) \text { for } k \geq 2$

Multiple Choice

Bode's sequence, defined by $a _ { 1 } = 0.4 , a _ { k } = 0.1 \left( 3 \cdot 2 ^ { k - 2 } + 4 \right) \text { for } k \geq 2$ can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 5th term of the sequence.

A) $a _ { 5 } = 4.1$
B) $a _ { 5 } = 2.3$
C) $a _ { 5 } = 3.2$
D) $a _ { 5 } = 2.8$
E) $a _ { 5 } = 6.8$