Q:

# 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}

Accepted Solution

A:
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 onOn 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