Sequences

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ACT Math › Sequences

Questions 1 - 10
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

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.

3

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.

4

If four consecutive odd integers greater than 9 are added together, what is the smallest possible sum of those four integers?

Explanation

The 4 consecutive of integers greater than 9 (but not including 9) are 11, 13, 15, 17. Added together, we get 56.

5

If four consecutive odd integers greater than 9 are added together, what is the smallest possible sum of those four integers?

Explanation

The 4 consecutive of integers greater than 9 (but not including 9) are 11, 13, 15, 17. Added together, we get 56.

6

If four consecutive odd integers greater than 9 are added together, what is the smallest possible sum of those four integers?

Explanation

The 4 consecutive of integers greater than 9 (but not including 9) are 11, 13, 15, 17. Added together, we get 56.

7

What is the next term in the sequence:

Explanation

Because it is an arithmetic sequence, the difference between each term is the same. Therefore find out the difference between any two consecutive terms. and so the sequence increases by 5 each term. Thus the answer is .

8

What is the th term in the following series of numbers: ?

148

Explanation

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .

9

What is the th term in the following series of numbers: ?

148

Explanation

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .

10

What is the next term in the sequence:

Explanation

Because it is an arithmetic sequence, the difference between each term is the same. Therefore find out the difference between any two consecutive terms. and so the sequence increases by 5 each term. Thus the answer is .

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