Worked example
Find the sum of the first 5 terms of an arithmetic sequence whose first term is 2 and common difference is 3.
Answer & why
Answer: 40
The last term is 14. Sum = 5(2+14)/2 = 40.
Grade 10 · Math
Sum an arithmetic sequence
Use equal-sum pairs to find a finite arithmetic series.
8 authored questions + worked example
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All questions
All 8 authored questions for this skill.
Question 1
Find the sum of the first 5 terms of an arithmetic sequence whose first term is 7 and common difference is 4.
- 74
- 77
- 75
- 76
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 75
The last term is 23. Sum = 5(7+23)/2 = 75.
Question 2
Find the sum of the first 6 terms of an arithmetic sequence whose first term is 8 and common difference is 3.
- 93
- 92
- 95
- 94
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 93
The last term is 23. Sum = 6(8+23)/2 = 93.
Question 3
Find the sum of the first 5 terms of an arithmetic sequence whose first term is 2 and common difference is 3.
- 40
- 42
- 39
- 41
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 40
The last term is 14. Sum = 5(2+14)/2 = 40.
Question 4
Find the sum of the first 8 terms of an arithmetic sequence whose first term is 4 and common difference is 2.
- 88
- 90
- 87
- 89
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 88
The last term is 18. Sum = 8(4+18)/2 = 88.
Question 5
Find the sum of the first 6 terms of an arithmetic sequence whose first term is 3 and common difference is 4.
- 79
- 77
- 80
- 78
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 78
The last term is 23. Sum = 6(3+23)/2 = 78.
Question 6
Find the sum of the first 7 terms of an arithmetic sequence whose first term is 5 and common difference is 3.
- 98
- 100
- 99
- 97
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 98
The last term is 23. Sum = 7(5+23)/2 = 98.
Question 7
Find the sum of the first 9 terms of an arithmetic sequence whose first term is 6 and common difference is 2.
- 128
- 125
- 126
- 127
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 126
The last term is 22. Sum = 9(6+22)/2 = 126.
Question 8
Find the sum of the first 8 terms of an arithmetic sequence whose first term is 1 and common difference is 5.
- 148
- 147
- 150
- 149
A hint
Pair the first and last terms; each pair has the same total.
Answer & why
Answer: 148
The last term is 36. Sum = 8(1+36)/2 = 148.