Question

For the following exercises, write the first four terms of the sequence.

Answer 1

Consider the explicit formula of a sequence,

an = (2n + 1)/n3 ...... (1)

 

Compute first term of the sequence by substituting n = 1 in formula (1),

a1 = (2 × 1 + 1)/13

      = 3/1

     = 3

 

Compute second term of the sequence by substituting n = 2 in formula (1),

a2 = (2 × 2 + 1)/23

     = 5/8

 

Compute third term of the sequence by substituting n = 3 in formula (1),

a3 = (2 × 3 + 1)/33

     = 7/27

 

Compute forth term of the sequence by substituting n = 4 in formula (1),

a4 = (2 × 4 + 1)/43

     = 9/64

 

Therefore, the first four terms of the given sequence are {3, 5/8, 7/27, 9.64}.

Therefore, the first four terms of the given sequence are {3, 5/8, 7/27, 9.64}.