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CARD 5:
A sequence can be generated using the formula shown below.

{:[f(1)=26],[f(n)=f(n-1)+13]:}
Harvey says the common difference is 13.
Heather says the value of
f(4) is 52 .
Harvey
Heather

CARD $5$ : $\newline$ A sequence can be generated using the formula shown below. $\newline$ $\begin{array}{c} f(1)=26 \\ f(n)=f(n-1)+13 \end{array}$ $\newline$ Harvey says the common difference is $13$ . $\newline$ Heather says the value of $f(4)$ is $52$ . $\newline$ Harvey $\newline$ Heather

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Write and solve inverse variation equations

Full solution

Q. CARD

5

:

\newline

A sequence can be generated using the formula shown below.

\newline

\begin{array}{c} f(1)=26 \\ f(n)=f(n-1)+13 \end{array}

\newline

Harvey says the common difference is

13

.

\newline

Heather says the value of

f(4)

is

52

.

\newline

Harvey

\newline

Heather

Check Common Difference: Harvey says the common difference is $13$ . Let's check the formula for the sequence to see if he's right. $\newline$ $f(n) = f(n-1) + 13$ means that each term is $13$ more than the previous term. $\newline$ So, the common difference is indeed $13$ .
Calculate $f(4)$ : Heather says the value of $f(4)$ is $52$ . Let's calculate $f(4)$ using the formula. $\newline$ $f(1) = 26$ $\newline$ $f(2) = f(1) + 13 = 26 + 13 = 39$ $\newline$ $f(3) = f(2) + 13 = 39 + 13 = 52$ $\newline$ $f(4) = f(3) + 13 = 52 + 13 = 65$ $\newline$ Oops, Heather's claim that $f(4)$ is $52$ is incorrect.

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