# Worksheet: Sum of a Finite Arithmetic Series

In this worksheet, we will practice finding the sum of a finite arithmetic series or the nth partial sum of an infinite arithmetic series to a particular term.

**Q4: **

Find the sum of the second half of terms of the sequence .

**Q6: **

Find the sum of the last third of the terms in the sequence .

**Q7: **

Find the largest sum of the arithmetic sequence .

**Q8: **

Find the smallest sum for the arithmetic sequence .

**Q9: **

Find the value of the series .

**Q10: **

Find the sum of the integers between 4 and 57 that are divisible by 5.

- A275
- B390
- C455
- D330

**Q11: **

A fast food restaurant offers to give away two £100-prizes on one day. They will give away four £100-prizes the next day, six £100-prizes the next day, and so on, giving away two more £100-prizes each day than the previous day. If represents the number of days in their campaign, find a formula to calculate how many pounds they will they have given away in total by the end of the campaign.

- A
- B
- C
- D
- E

**Q12: **

A boulder rolled down a mountain, gaining speed. It traveled 6 feet in the first second, and, in each successive second, it traveled 8 feet more than the previous second. How far did the boulder travel after 10 seconds?

**Q13: **

On New Year’s Eve, Sherif decided he wanted to do a lot more exercise. On the 1st of January, he would do one press-up. On the 2nd of January, he would do two press-ups. On the 3rd of January, he would do three press-ups and then he would carry on adding an extra press-up each day for a whole year. Assuming that he kept to his plan and that the next year was not a leap year, how many press-ups did he do throughout the entire year?

**Q14: **

Using that is the sum of the first terms of an arithmetic sequence with term , decide if the following statement is correct:

To find the greatest sum of terms of an arithmetic sequence, we first find the number of positive terms by finding the largest integer for which , and then calculate which is the greatest sum.

- ACorrect
- BNot correct

**Q15: **

A fast food restaurant offers to give away two prizes on June 1st. They will give away four prizes on June 2nd, six prizes on June 3rd, and so on, giving away two more prizes each day than the previous day. How much money will they have given away in total by the end of June?

**Q16: **

Find an expression for the sum of an arithmetic sequence whose first term is and whose common difference is .

- A
- B
- C
- D
- E

**Q17: **

An arithmetic sequence has 20 terms; its first term is 2 and its last term is 21. Find the sum of the terms of the sequence.

**Q18: **

A fast food restaurant offers to give away two prizes on July 1st. They will give away four prizes on July 2nd, six prizes on July 3rd, and so on, giving away two more prizes each day than the previous day. How much money will they have given away in total by the end of July?

**Q19: **

Fady saves £1 on the first day, £2 on the second day, £3 on the third day, and so on, saving an extra each day. On which day will he have saved over £100 in total?

**Q20: **

Write an expression for the sum of the first terms of an arithmetic sequence with first term and last term .

- A
- B
- C
- D
- E

**Q21: **

Find using properties of summation and given and .