Question

Which of the following best defines the sequence shown? 7, 16, 25, 34....f(1) = 7, f(n) = f(n-1) - 9f(1) = 7, f(n) = f(n-1) - 16f(1) = 7 f(n) = f(n-1) + 16 f(1) = 7 f(n) = f(n-1) + 9

Answer 1

The general form of an arithmetic sequence can be written as:

`a(n)=a+(n-1)d`

Where

a is the first term

d is the common difference [difference between a term and its preceeding term]

• The first term is 7

Thus,

a = 7

• The common difference between the terms is:

16 - 7 = 9

25 - 16 = 9

34 - 25 = 9

Thus,

common difference is 9

d = 9

Plugging into the equation we have:

`\begin{gathered} a(n)=7+(n-1)(9) \\ a(n)=7+9n-9 \\ a(n)=9n-2 \end{gathered}`

This question gives the information in a different notation, that's all.

We match it with our solution.

a(1), or f(1) is the first term, which is 7.

The formula given is in terms of f(n-1).

f(n-1) is the term before it

So, we have:

f(n) = term before it + WHAT???

We know that to get the next term [ f(n) }, we have to ADD 9 to the term before it [ f(n-1) ].

Thus,

f(n) = f(n-1) + 9

Looking at the answer choices, the last one is correct.

Correct Answer:

f(1) = 7; f(n) = f(n-1) + 9​