Question

Following one side of a new street in a neighbourhood, the house numbers increase by six. The house number of the first house on the street is 319. Express this sequence recursively and explicitly. 

https://i.gyazo.com/d767c3f3326c6bf29fb188a8c2bec5f1.png 

Answer 1

If the first house number is represented by \(a_{1}=319\)

Then

$$ \begin{aligned} &a_{2}=a_{1}+6=319+6=325 \\ &a_{3}=a_{2}+6=325+6=331 \\ &a_{4}=a_{3}+6=331+6=337 \\ &\vdots \end{aligned} $$

$$ a_{n}=a_{n-1}+6 \text { is the sequence in recursive form. } $$

Let the first number of the sequence be \(a\)

Given, \(a=319\)

According to the question the common difference \(d=6\) \(n^{t h}\) term of the sequence is given by:

$$ \begin{aligned} &a_{n}=a+d(n-1) \\ &a_{n}=319+6(n-1) \\ &a_{n}=319+6 n-6 \end{aligned} $$

\(a_{n}=313+6 n\) is the sequence in explicit forn.