Sequences: Determine the first five terms of the following sequences: A. a_(n) = (2n+3)/(4) B. a_(n) = (n-3)/(n-2)

Question

Sequences:

Determine the first five terms of the following sequences:

A.
`a_(n) = (2n+3)/(4)`

B.
`a_(n) = (n-3)/(n-2)`

Answer 1

A.

• aₙ = (2n + 3)/4

The first 5 terms:

• a₁ = (2*1 + 3) / 4 = 5/4
• a₂ = (2*2 + 3) / 4 = 7/4
• a₃ = (2*3 + 3)/ 4 = 9/4
• a₄ = (2*4 + 3) / 4 = 11/4
• a₅ = (2*5 + 3) / 4 = 13/4

B.

• aₙ = (n - 3)/(n - 2)

The first 5 terms:

• a₁ = (1 - 3) / (1 - 2) = 2
• a₂ = (2 - 3) / (2 - 2) = undefined
• a₃ = (3 - 3)/ (3 - 2) = 0
• a₄ = (4 - 3) / (4 - 2) = 1 / 2
• a₅ = (5 - 3) / (5 - 2) = 2 / 3