The 5th term of 3, 7, 11, ... is 19 and the sum of an arithmetic sequence is S = n ÷ 2 (2a + (n − 1)d), so this Year 13 sheet opens with one stored term and the general sum. The answers record 3 and 2 among the sequence values.
Key Takeaways
The 5th term of 3, 7, 11, ... is 19 (Q1).
The arithmetic sum is S = n ÷ 2 (2a + (n − 1)d) (Q2).
Q3 records 3 among the sequence answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The 5th term of the arithmetic sequence 3, 7, 11, ... is:
(a) 19(b) 15(c) 23(d) 18
2.The sum of the first n terms of an arithmetic sequence with first term a and common difference d is:
(a) S = n ÷ 2 (2a + (n − 1)d)(b) S = n(a + (n − 1)d)(c) S = a + (n − 1)d(d) S = n ÷ 2 (a + (n − 1)d)
3.The common ratio of the geometric sequence 2, 6, 18, ... is:
(a) 3(b) 4(c) 2(d) 6
4.The sum to infinity of the geometric series 1 + ½ + ¼ + ... is:
(a) 2(b) 1(c) 3(d) ½
5.The third term in the binomial expansion of (1 + x)⁴ is:
(a) 6x²(b) 4x²(c) x²(d) 4x³
6.The sum of the first five terms of the geometric sequence 1, 2, 4, 8, ... is:
(a) 31(b) 32(c) 15(d) 30
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the 10th term of the arithmetic sequence 5, 8, 11, ...
8.Evaluate 1 + 2 + 3 + ... + 100.
9.For the geometric sequence 3, 6, 12, ..., write down the common ratio and find the 7th term.
10.Find the sum to infinity of the geometric series 8, 4, 2, ...
11.Write down the full binomial expansion of (1 + x)⁴.
12.In an arithmetic sequence, the 5th term is 17 and the 9th term is 33. Find the first term and the common difference.
13.Evaluate the sum 2 + 6 + 18 + 54.
14.Evaluate Σ (r = 1 to 5) r, the sum of the first five positive integers.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A student saves £5 in week 1 and increases the amount saved by £3 each week. Find the total amount saved after 10 weeks.
16.A population of bacteria doubles every hour and starts with 100 bacteria. Find the population after 5 hours.
17.A ball is dropped from a height of 10 m and rebounds to half its previous height on each bounce. Find the total distance travelled before it comes to rest.
18.A geometric sequence has first term 4 and third term 36. Find the two possible values of the common ratio.
19.An arithmetic sequence has first term 10 and the sum of its first 10 terms is 235. Find the common difference.
20.The sum to infinity of a geometric series is 18 and its first term is 6. Find the common ratio.
Answer Key
1. a) 19
2. a) S = n ÷ 2 (2a + (n − 1)d)
3. a) 3
4. a) 2
5. a) 6x²
6. a) 31
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the 5th term of 3, 7, 11, ...?
19, option (a) in this worksheet (Q1).
What is the sum of the first n arithmetic terms?
S = n ÷ 2 (2a + (n − 1)d), option (a) in this worksheet (Q2).
What is the common difference of 3, 7, 11, ...?
4, recorded among the answers of this worksheet.
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