MATH SOLVE

6 months ago

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 [tex]a_{n}=3+a_{n-1}[/tex]Solution:The given sequence is :- 8, 11, 14, 17, 20, 23, 26, .....[tex]\text { The first term is } a_{1}=8[/tex]Second term is [tex]a_2 = 11[/tex] 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:[tex]a_{n}=3+a_{n-1}[/tex]Let's check the above recursive definition by substituting n = 2 we should get 11[tex]a_2 = 3 + a_{2-1}\\\\a_2 = 3 + a_{1}\\\\a_2 = 3 + 8 = 11[/tex]Thus the required recursive definition is found