Question

Which function represents the sequence –7.25, –6.75, –6.25, –5.75, … ? A. B. C. D.

Answer 1

You are adding by 0.50 every time because when you are working with negative numbers, adding makes the value of the negative number smaller.

Answer 2

Answer: $S_n = -7.25 + 0.5(n - 1)$
Explanation: Let's form the arithmetic progression. For the sequence, not the sum, we use this form:

$S_n = a + (n - 1)d$, a is the first term and d is the common difference.
Now each term goes up by 0.5, so d is 0.5

Substituting everything in, we get:
$S_n = -7.25 + (n - 1)(0.5)$

and we can verify this is true if we substitute n = 2, for -6.75 and so on.