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Mathbound · Contest practice

Arithmetic Sequences worksheet

Mixed difficulty

Name

Date

1.
What is the sum of the first $7$ positive integers?
- A.49
- B.28
- C.27
- D.35
- E.14
2.
What is the sum of the first $9$ positive integers?
- A.81
- B.45
- C.44
- D.54
- E.18
3.
What is the sum of the first $22$ positive integers?
- A.275
- B.44
- C.484
- D.253
- E.252
4.
Arithmetic sequence: first term $2$ , common difference $7$ . Sum of first $12$ terms?
- A.79
- B.486
- C.479
- D.498
- E.24
5.
The sum of the first $n$ positives is $210$ . Find $n$ .
- A.21
- B.20
- C.22
- D.18
- E.19
6.
Arithmetic sequence: first term $4$ , common difference $6$ . Sum of first $25$ terms?
- A.148
- B.1900
- C.1894
- D.1925
- E.100
7.
Arithmetic sequence: first term $2$ , common difference $7$ . Sum of first $15$ terms?
- A.100
- B.765
- C.758
- D.780
- E.30
8.
Arithmetic sequence: first term $4$ , common difference $2$ . Sum of first $15$ terms?
- A.285
- B.60
- C.32
- D.270
- E.268
9.
Arithmetic sequence: first term $4$ , common difference $5$ . Sum of first $15$ terms?
- A.600
- B.60
- C.74
- D.585
- E.580
10.
What is the sum of the first $11$ positive integers?
- A.66
- B.65
- C.77
- D.22
- E.121

Answer key · worked solutions

1. B. 28
$n(n+1)/2$ . $7(7+1)/2$ . $28$ .
2. B. 45
$n(n+1)/2$ . $9(9+1)/2$ . $45$ .
3. D. 253
$n(n+1)/2$ . $22(22+1)/2$ . $253$ .
4. B. 486
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $486$ .
5. B. 20
$n(n+1)/2=210$ . $n=20$ . $20$ .
6. B. 1900
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $1900$ .
7. B. 765
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $765$ .
8. D. 270
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $270$ .
9. D. 585
$S_n=\frac n2(2a+(n-1)d)$ . Plug values. $585$ .
10. A. 66
$n(n+1)/2$ . $11(11+1)/2$ . $66$ .

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