Question

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

Answer 1

Answer:

$a_1 = 2$

$a_2 = 3$

$a_3 = 5$

$a_4 = 8$

$a_5 = 13$

Step-by-step 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:

$a_n = a_{n-1} + a_{n-2}$

$a_5 = a_{5-1} +a_{5-2}$

$a_5 = a_4 +a_3$

$a_5 = 8+5$

$a_5 = 13$