$n$ $1$ $2$ $3$ $4$
$f (n)$ $- 2$ $1$ $4$ $7$
The table above shows some values of the linear function $f$ . Which of the following defines $f$ ?

f (n) = n - 3

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f (n) = 2 n - 4

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f (n) = 3 n - 5

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f (n) = 4 n - 6

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Solution

The correct option is B $f (n) = 3 n - 5$
Let the linear function be $f (n) = a n + b$
Given, $f (1) = - 2$
$\Rightarrow - 2 = a + b$ ...(i)
Again, $f (2) = 1$
$\Rightarrow 1 = 2 a + b$ ...(ii)
On subtracting (ii) from (i)
$a = 3$
From (i) $b = - 5$
$∴ f (n) = 3 n - 5$
Hence, option C is correct.

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