How to find the common difference in sequences

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ACT Math › How to find the common difference in sequences

Questions 1 - 5

1

In the sequence 3, ____, ____, 24, what numbers can fill the two blanks so that consecutive terms differ by a common ratio?

6, 12

9, 18

10, 15

10, 17

12, 16

Explanation

If the common ratio is r, then the sequence can be rewritten as 3, 3r, , . We see then that , which gives us that r=2. Therefore, the missing terms are 6 and 12.

2

Find the common difference of the following sequence:

Explanation

The common difference is equal to

$a_{n+1}:-:a_{n}$ .

Plugging in the values from this problem we get,

$\vdots$

Therefore, in this case the common difference is .

3

The following is an arithmetic sequence. Find an explicit equation for it in terms of the common difference.

${\large} 3, 7, 11, 15, 19,...{}$

${\large} a_n = 4n-1$

${\large} a_n=3n+1$

${\large} a_n=3n$

${\large} a_n=4n+2$

Explanation

Finding the common difference is fairly simple. We simply subtract the first term from the second. 7-3 = 4, so 4 is our common difference. So each term is going to be 4n plus something:

${\large} a_n = 4n+x$

We know the first term is 3, so we can plug in that to our equation.

${\large} 3=4+x$

$\large x=-1$

So the explicit form of our arithmetic sequence is

${\large} a_n=4n-1$ .

4

Find the common difference of the following sequence:

Explanation

The common difference is equal to

$a_{n+1}:-:a_{n}$ .

Plugging in the values from this problem we get,

$\vdots$

Therefore, in this case the common difference is .

5

Find the common difference of the following sequence:

Explanation

The common difference is equal to

$a_{n+1}:-:a_{n}$

Plugging our values into this equation we can find the common difference.

$\vdots$

Therefore, in this case the common difference is .

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