Sequences

Correct answer: B. 17

Explanation: The terms of the sequence are 2, 7, 12, and 17 in order. Therefore, the fourth term is 17. Here, 12 is the third term, while 22 would be the next, or fifth, term. Exam tip: When asked for a term number in a sequence, count the terms from left to right.

Correct answer: C. 45

Explanation: The difference between each pair of consecutive terms is 5: 30−25=5, 35−30=5, and 40−35=5. Therefore, adding 5 to 40 gives the next term, 45. Option 44 is not correct because it would give a difference of 4. Exam tip: To find the next term, first check the difference between consecutive terms.

Correct answer: B. 6

Explanation: Each term is 3 less than the preceding term: 18, 15, 12, 9. Therefore, subtracting 3 from 9 gives the next term as 6. Choosing 7 would give a difference of 2, which does not match the constant difference in the sequence. Exam tip: Compare consecutive terms to identify the pattern before finding the next term.

Correct answer: C. 24

Explanation: Each successive term is obtained by adding 5: 4, 9, 14, 19, 24. Therefore, the fifth term is 24. The number 25 would be the next (sixth) term. Exam tip: Write and count the terms in order to avoid mistakes in sequence questions.

Correct answer: C. 16

Explanation: Each successive term decreases by 4: 32, 28, 24, 20, 16. Therefore, the fifth term is 16. Getting 18 would require subtracting only 2 from 20, which does not follow the common difference of the sequence. Exam tip: Find the difference between consecutive terms first, then continue the same pattern.

Correct answer: C. 21

Explanation: Each term in the sequence is 5 more than the previous term: 1, 6, 11, 16. Therefore, the next term is \(16+5=21\). Choosing 20 would give a difference of 4, which does not match the common difference of the given sequence. Exam tip: Find the difference between consecutive terms to identify the pattern.

Correct answer: B. 50

Explanation: Each term in the sequence is 5 less than the preceding term: 70, 65, 60, 55. Therefore, 55 - 5 = 50, so 50 is the correct answer. Option 54 is only 1 less than 55 and does not follow the pattern. Exam tip: Find the difference between consecutive terms to identify the rule of a sequence.

Correct answer: C. 23

Explanation: Each successive term is obtained by adding 5: 3, 8, 13, 18, 23. Therefore, the fifth term is 23. Option 24 would result from adding 6 to 18, which does not follow the pattern. Exam tip: count the given terms in order and add the common difference for the next term.

Correct answer: C. 36

Explanation: Each successive term decreases by 6: 60, 54, 48, 42. Therefore, the next term is \(42-6=36\). Choosing 38 would mean a decrease of 4, which does not follow the pattern. Exam tip: Check the difference between consecutive terms before finding the next term.

Correct answer: D. 23

Explanation: This is an arithmetic sequence in which each successive term increases by 3. The terms are 8, 11, 14, 17, 20, 23. Therefore, the sixth term is 23. Option 20 is the fifth term, so it is a close but incorrect distractor. Exam tip: Write the terms in order and count their positions carefully.

Correct answer: B. 25

Explanation: Each successive term is 5 less than the previous term: 45, 40, 35, 30, 25. Therefore, the fifth term is 25. The number 30 is the fourth term, so it is not correct. Exam tip: Write the term numbers while counting to avoid such errors.

Correct answer: C. 30

Explanation: Each term is obtained by adding 5 to the previous term: 10, 15, 20, 25. Therefore, the term after 25 is \(25+5=30\). Choosing 28 or 29 would not maintain the common difference of 5. Exam tip: Find the difference between consecutive terms to identify the next term in a sequence.

Correct answer: C. 18

Explanation: Each successive term is 2 less than the preceding term: 26, 24, 22, 20. Therefore, 20 - 2 = 18, so 18 is the correct answer. 19 is not correct because it is only 1 less than 20. Exam tip: Find the difference between consecutive terms to identify the next term in a sequence.

Correct answer: C. 36

Explanation: Each successive term is 6 greater than the previous term: 12, 18, 24, 30, 36. Therefore, the fifth term is 36. Choosing 34 would not follow the common difference of 6. Exam tip: List the terms in order and count their positions to avoid confusing the fourth and fifth terms.

Correct answer: D. 45

Explanation: Each term is 9 less than the previous term: 81, 72, 63, 54. Therefore, the next term is \(54-9=45\). Choosing 48 would mean a decrease of 6, whereas the common difference in the sequence is 9. Exam tip: Find the difference between consecutive terms to identify the pattern.

Correct answer: C. 25

Explanation: This is an arithmetic sequence because 4 is added to each term. The fifth term is 21, so the sixth term is 25. Hence, 25 is correct. The value 23 would result from adding 6 to 17, which does not follow the common difference. Exam tip: List the terms in order or use \(a_n=a+(n-1)d\) to verify the required term.

Correct answer: B. 21

Explanation: Each term is obtained by subtracting 3 from the previous term: 33, 30, 27, 24. Therefore, 24 - 3 = 21, so the next term is 21. The option 22 would result from subtracting 2, which does not follow the given pattern. Exam tip: Compare consecutive terms to identify the rule of a sequence.

Correct answer: C. 27

Explanation: Each consecutive term increases by 5: 7, 12, 17, 22, 27. Therefore, the fifth term is 27. Option 26 is not correct because adding 5 to the fourth term, 22, gives 27. Exam tip: Check the common difference between consecutive terms to find the next term.

Correct answer: C. 24

Explanation: Each consecutive term decreases by 6: 48 to 42, 42 to 36, and 36 to 30. Therefore, the next term is \(30-6=24\). Choosing 25 would give a decrease of 5, which does not follow the pattern. Exam tip: Check the difference between consecutive terms before finding the next term.

Correct answer: C. 34

Explanation: In this sequence, each successive term is 4 greater than the previous term. The terms are 14, 18, 22, 26, 30, 34. Therefore, the sixth term is 34. Although 30 is close, it is the fifth term. Exam tip: Write the terms in order and count their positions carefully.

Correct answer: C. 12

Explanation: Each term in the sequence is 2 less than the previous term: 20, 18, 16, 14. Therefore, 14 - 2 = 12, so 12 is the correct answer. Choosing 13 would give a difference of 1, which does not match the pattern. Exam tip: Find the difference between consecutive terms before predicting the next term.

Correct answer: B. 21

Explanation: Each successive term is obtained by adding 3: 9, 12, 15, 18, 21. Therefore, the fifth term is 21. Option 20 is not possible because adding 3 to 18 gives 21. Exam tip: Count the terms in order and check the common difference.

Correct answer: C. 40

Explanation: Each term is 8 less than the preceding term: 72 to 64, 64 to 56, and 56 to 48. Therefore, the next term is \(48-8=40\). Option 41 would result from subtracting 7, but the common difference of this sequence is \(-8\). Exam tip: Find the difference between consecutive terms to identify the rule of a sequence.

Correct answer: C. 32

Explanation: The sequence increases by 4 at each step: 16, 20, 24, 28, 32. Therefore, the fifth term is 32. Choosing 30 would use an increase of 2, which does not match the common difference of 4 in the given sequence. Exam tip: To find the next term, first check the difference between consecutive terms.

Correct answer: C. 30

Explanation: Each consecutive term in the sequence decreases by 6: 54, 48, 42, 36. Therefore, the next term is \(36-6=30\). Choosing 31 would not keep the common difference the same. Exam tip: Check the difference between consecutive terms before finding the next term.