Consider the sequence: 8, 11, 14, 17, 20, 23, 26, The recursive definition is ![a_{n}=3+a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D3%2Ba_%7Bn-1%7D)
<h3><u>Solution:</u></h3>
The given sequence is :- 8, 11, 14, 17, 20, 23, 26, .....
![\text { The first term is } a_{1}=8](https://tex.z-dn.net/?f=%5Ctext%20%7B%20The%20first%20term%20is%20%7D%20a_%7B1%7D%3D8)
Second term is
and so on
On analyzing the above series we can say
<em><u>Each time we want a new term, we add on 3 to previous term which is as follows:-
</u></em>
8 + 3 = 11
11 + 3 = 14
14 + 3 = 17
17 + 3 = 20
20 + 3 = 23
23 + 3 = 26
And so on
<em><u>This recursive step of adding on 3 to the prior term is written in the following general form:</u></em>
![a_{n}=3+a_{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3D3%2Ba_%7Bn-1%7D)
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](https://tex.z-dn.net/?f=a_2%20%3D%203%20%2B%20a_%7B2-1%7D%5C%5C%5C%5Ca_2%20%3D%203%20%2B%20a_%7B1%7D%5C%5C%5C%5Ca_2%20%3D%203%20%2B%208%20%3D%2011)
Thus the required recursive definition is found