Sequences

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The difference between consecutive terms is 3: 6−3=3, 9−6=3, and 12−9=3. Therefore, adding 3 to 12 gives the next term, 15. The number 18 would come after adding 3 twice from 12. Exam tip: Check the difference between consecutive terms before finding the next term.

Check the difference between consecutive terms: 22 - 25 = -3, 19 - 22 = -3, and 16 - 19 = -3. Thus, each next term is obtained by subtracting 3. Therefore, 16 - 3 = 13, so 13 is correct. Choosing 14 would mean a decrease of only 2. Exam tip: Before finding the next term, check the difference between consecutive terms.

In this sequence, each term is twice the previous term: 2, 4, 8, 16. Therefore, the next term is \(16\times 2=32\). Although 24 is obtained by adding 8 to 16, the differences are 2, 4, and 8, so they are not constant. Exam tip: first check whether consecutive terms are related by multiplication or division.

The given terms are consecutive square numbers: \(1=1^2\), \(4=2^2\), \(9=3^2\), and \(16=4^2\). Therefore, the next term is \(5^2=25\). \(24\) is not correct because it is not a perfect square. Exam tip: In a sequence of square numbers, the successive differences are odd numbers: \(3,5,7,9,\ldots\).

The differences between consecutive terms are 6−2=4, 12−6=6, and 20−12=8. Since each difference increases by 2, the next difference is 10. Therefore, the next term is 20+10=30. Choosing 28 would give a difference of only 8, which does not continue the pattern of increasing differences. Exam tip: For such sequences, first list the consecutive differences and check their pattern.

In this sequence, each term is twice the preceding term: 5 to 10, 10 to 20, and 20 to 40. Therefore, the next term is \(40 \times 2 = 80\). Although 60 is obtained by adding 20 to 40, the differences are not constant here; the pattern is multiplication by 2. Exam tip: For a sequence, first check consecutive differences and then check consecutive ratios.

In this sequence, each term is obtained by dividing the previous term by 2: 64, 32, 16, 8. Therefore, the next term is \(8 \div 2=4\). The number 2 would be obtained after halving 8 twice, so it is not the next term. Exam tip: First check for a common multiplication or division rule between consecutive terms.

Each term in the sequence is 3 greater than the previous term: 10, 13, 16, 19, 22. Therefore, the missing term after 16 is 19. Choosing 18 would not maintain the common difference of 3. Exam tip: For a missing-term sequence, first check the difference between consecutive known terms.

Each term in the sequence is obtained by adding 7: 7, 14, 21, 28, 35. Therefore, the missing term is 21. If 20 were used, the increase from 14 to 20 would be 6, so the common difference would not remain the same. Exam tip: For a missing-term sequence, compare consecutive known terms to identify the rule.

Each successive term is 5 less than the preceding term: 40, 35, 30, 25, 20. Therefore, the missing term after 40 is 35. If 34 were chosen, the difference from 40 would be 6, so the sequence rule would not be followed. Exam tip: Compare consecutive known terms to identify the common difference in a sequence.