Question

For the sequence an = an-1 + an-2 and ai = 2, a2 = 3,

its first term is
its second term is
its third term is
its fourth term is
its fifth term is

Answer 1

`a_1 = 2`

`a_2 = 3`

`a_3 = 5`

`a_4 = 8`

`a_5 = 13`

Explanation:

Given

`a_n = a_(n-1) + a_(n-2)`

`a_1 = 2`

`a_2 = 3`

Solving (a): The first term

This has already been given as:

`a_1 = 2`

Solving (b): The second term

This has already been given as:

`a_2 = 3`

Solving (c): The third term

This is calculated as:

`a_n = a_(n-1) + a_(n-2)`

`a_3 = a_(3-1) +a_(3-2)`

`a_3 = a_2 +a_1`

`a_3 = 3 +2`

`a_3 = 5`

Solving (d): The fourth term

This is calculated as:

`a_n = a_(n-1) + a_(n-2)`

`a_4 = a_(4-1) +a_(4-2)`

`a_4 = a_3 +a_2`

`a_4 = 5+3`

`a_4 = 8`

Solving (e): The fifth term

This is calculated as:

`a_n = a_(n-1) + a_(n-2)`

`a_5 = a_(5-1) +a_(5-2)`

`a_5 = a_4 +a_3`

`a_5 = 8+5`

`a_5 = 13`