Question

Consider the sequence: 8, 11, 14, 17, 20, 23, 26, ..... Write a recursive definition: Group of answer choices
LaTeX: a_n=2\cdot a_{n-1}-5 a n = 2 ⋅ a n − 1 − 5
LaTeX: a_n=3\cdot a_{n-1} a n = 3 ⋅ a n − 1
LaTeX: a_n=3+a_{n-1} a n = 3 + a n − 1
LaTeX: a_n=8+3\cdot a_{n-1}

Answer 1

Consider the sequence: 8, 11, 14, 17, 20, 23, 26, The recursive definition is $a_{n}=3+a_{n-1}$

Solution:

The given sequence is :- 8, 11, 14, 17, 20, 23, 26, .....

$\text { The first term is } a_{1}=8$

Second term is $a_2 = 11$ and so on

On analyzing the above series we can say  

Each time we want a new term, we add on 3 to previous term which is as follows:-

8 + 3 = 11

11 + 3 = 14

14 + 3 = 17

17 + 3 = 20

20 + 3 = 23

23 + 3 = 26

And so on

This recursive step of adding on 3 to the prior term is written in the following general form:

$a_{n}=3+a_{n-1}$

Let's check the above recursive definition by substituting n = 2 we should get 11

$a_2 = 3 + a_{2-1}\\\\a_2 = 3 + a_{1}\\\\a_2 = 3 + 8 = 11$

Thus the required recursive definition is found