Question

1. Which best describes the relationship between the successive terms in the sequence shown?

9, –1, –11, –21, …

a)The common difference is –10.
b)The common difference is 10.
c)The common ratio is –9.
d)The common ratio is 9.

2. A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?

a)1, –5, 25, –125, ...
b)2, 10, 50, 250, ...
c)3, –2, –7, –12, ...
d)4, 9, 14, 19, ...

Answer 1

The answer is A.) The common difference is -10

Answer 2

Q1. The answer is a)The common difference is –10.

Let's calculate the common difference (c):
c = f(n + 1) - f(n)

9, –1, –11, –21, …
-1 - 9 = -10
-11 - (-1) = -11 + 1 = -10
-21 - (-11) = -21 + 11 = -10


Q2. The answer is c)3, –2, –7, –12, ...

f(n + 1) = f(n) – 5
f(n + 1) - f(n) = -5

c = f(n + 1) - f(n)

So, the common difference is: c = -5

Let's check all choices:
a) c = -5 - (-1) = -5 + 1 = -4 INCORRECT
b) c = 10 - 2 = 8 INCORRECT
c) c = -2 - (-3) = -5
c = -7 - (-2) = -5
c = -12 - (-7) = -5 CORRECT
d) c = 9 - 4 = 5 INCORRECT