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Worksheet: Sum of a Finite Arithmetic Series

Q1:

Find the sum of the arithmetic series 3 + 6 + 9 + + 3 3 .

Q2:

Find the sum of the arithmetic series 6 + 9 + 1 2 + + 3 6 .

Q3:

Find the sum of the arithmetic series 1 3 + 1 9 + 2 5 + + 8 5 .

Q4:

Find the sum of the first 17 terms of the arithmetic series 1 2 + 2 1 + 3 0 + .

Q5:

Find the sum of the first 18 terms of the arithmetic series 8 + 1 0 + 1 2 + .

Q6:

Find the sum of the first 26 terms of the arithmetic series 7 + 8 + 9 + .

Q7:

Find the sum of the arithmetic series 2 2 3 2 9 2 .

  • A 3 0 2
  • B 3 6 2
  • C 2 0 2
  • D 2 4 2
  • E 4 8 3

Q8:

Find the sum of the arithmetic series 5 5 3 5 3 9 5 .

  • A 4 2 0 5
  • B 4 4 1 5
  • C 3 8 0 5
  • D 3 9 9 5
  • E 3 9 9 1 0 5

Q9:

Chloe devised a week-long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and she will increase her study time by 30 minutes each successive day. How many total hours will Chloe have spent studying at the end of the week?

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 𝑛 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 𝑛 2 ( 2 𝑛 + 2 )
  • B 𝑛 ( 𝑛 + 1 0 0 )
  • C ( 𝑛 1 ) 2 ( 2 𝑛 + 2 ) + ( 𝑛 + 1 )
  • D 1 0 0 ( 𝑛 + 𝑛 ) 2
  • E 1 0 0 𝑛 + 𝑛 2

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, Ethan 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:

Find the largest sum of the arithmetic sequence 1 1 7 , 1 0 9 , 1 0 1 , .

Q15:

Find the largest sum of the arithmetic sequence 1 1 5 , 1 0 7 , 9 9 , .

Q16:

Find the largest sum of the arithmetic sequence 1 1 7 , 1 0 1 , 8 5 , .

Q17:

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

Q18:

A fast food restaurant offers to give away two £ 1 0 0 prizes on June 1st. They will give away four £ 1 0 0 prizes on June 2nd, six £ 1 0 0 prizes on June 3rd, and so on, giving away two more £ 1 0 0 prizes each day than the previous day. How much money will they have given away in total by the end of June?

Q19:

Find the value of the series 3 1 1 5 1 1 5 + 3 2 1 5 2 1 5 + + 5 9 1 5 2 9 1 5 + 6 0 1 5 3 0 1 5 .

Q20:

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

  • A 𝑛 2 ( 2 𝑎 + ( 𝑛 + 1 ) 𝑑 )
  • B 1 2 ( 2 𝑎 + ( 𝑛 1 ) 𝑑 )
  • C 𝑛 2 ( 𝑎 + ( 𝑛 1 ) 𝑑 )
  • D 𝑛 2 ( 2 𝑎 + ( 𝑛 1 ) 𝑑 )
  • E 𝑛 2 ( 𝑎 + 2 ( 𝑛 1 ) 𝑑 )

Q21:

Find the sum of the second half of terms of the sequence ( 6 2 , 7 0 , 7 8 , , 1 5 0 ) .

Q22:

Find the sum of the second half of terms of the sequence ( 5 5 , 5 1 , 4 7 , , 1 9 ) .

Q23:

Find the sum of the last third of the terms in the sequence 7 8 , 8 6 , 9 4 , , 1 9 0 .

Q24:

Find the smallest sum for the arithmetic sequence 1 0 6 , 9 9 , 9 2 , .

Q25:

Find the smallest sum for the arithmetic sequence 1 0 5 , 1 0 4 , 1 0 3 , .