Question

15-20. Recursive Sequences A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.

19. $a_n=a_{n-1}+a_{n-2}\text{and}{a}_1=1, a_2=2$.

Short answer

The first five terms are 1, 2, 3, 5, 7.

Step-by-step solution

Step-1 – Given

The given sequence is$a_n=a_{n-1}+a_{n-2} \text{and} a_1=1, a_2=2$.

Step-2 – To determine

We have to find the first five terms of the given sequence.

Step-3 – Calculation

To find the first five terms of the sequence we’ll plug n = 1, 2, 3, 4 and 5 respectively in the given sequence.

$\begin{array}{l}\text{For}n=1,a_1=1\\ \text{For}n=2,a_2=2\\ \text{For}n=3,a_3=a_{3-1}+a_{3-2}=a_2+a_1=2+1=3\\ \text{For}n=4,a_4=a_{4-1}+a_{4-2}=a_3+a_2=3+2=5\\ \text{For}n=5,a_5=a_{5-1}+a_{5-2}=a_4+a_3=4+3=7\end{array}$

Hence, the first five terms are 1, 2, 3, 5, 7.