Question

Write a recursive sequence that represents the sequence defined by the followingexplicit formula:aan = 3 - 7(n − 1)

Answer 1

According to the given problem, the nth term of the sequence is given by,

$\begin{gathered} a_n=3-7(n-1) \\ a_n=3-7n+7 \\ a_n=10-7n \end{gathered}$

Substitute the values of n=0,1,2,3,....

$\begin{gathered} a_0=10-7(0)=10-0=10 \\ a_1=10-7(1)=10-7=3 \\ a_2=10-7(2)=10-14=-4 \\ a_3=10-7(3)=10-21=-11 \end{gathered}$

Thus, the sequence of obtained as,

$10,3,-4,-11,\ldots\ldots\ldots,(10-7n)$

So we can write,

$\begin{gathered} a_1=3 \\ a_n=10-7n \end{gathered}$