Question

What would a sub 7 equal, if a sub 1 equals 8 and a sub k+1 equals a sub k plus 3?

Answer 1

Let \[ a _{1}=8\] and \[a _{k+1}=a _{k}+3\] Determine \[a_{7}\]

Answer 2

This is known as a recursive function.

We are given that \(a_1 = 8\)

So How much does \(a_2\) equal?

Well we know that, \(a_{k+1} = a_k + 3\)

So, \(a_2 = a_{1+1} = a_1 + 3 = 8 + 3 = 11\) [Here k becomes 1]

Hence, now we have the value of \(a_2 = 11\).

Did you get this recursion?
Can you proceed? :)

Answer 3

\(\large { a_1=8\qquad a_{k+1}=a_k+3
\\ \quad \\

\begin{array}{ccrcllll}
term(k)&&value
\\\hline\\
{\color{brown}{ 1}}&a_1&8\\
{\color{brown}{ 2}}&a_{{\color{brown}{ 1}}+1}&a_{\color{brown}{ 1}}+3\to 8+3\to 11\\
{\color{brown}{ 3}}&a_{{\color{brown}{ 2}}+1}&a_{\color{brown}{ 2}}+3\to 11+3\to 14\\
4&a_{{\color{brown}{ 3}}+1}& a_{{\color{brown}{ 3}}}+3\to 14+3\to 17\\
...&...&...

\end{array} }\)

Answer 4

keep in mind that the notation \(\bf a_{k+1}\) just means, " the next term "

so \(\bf a_{k+1}=a_k+3\to \) whatever the "current term" is, +1, or next term, will be our "current value" + 3

Answer 5

oh okay! thank you both so much! @AkashdeepDeb @jdoe0001

Answer 6

yw

Answer 7

:)