Lesson Worksheet: Arithmetic Series Mathematics • 10th Grade

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In this worksheet, we will practice calculating the sum of the terms in an arithmetic sequence with a definite number of terms.

Q1:

Find the number of terms in the arithmetic sequence whose first term is 11 and last term is 81, where the sum of all the terms is 506.

Q2:

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

  • A𝑛2(2𝑎+(𝑛−1)𝑑)
  • B𝑛2(2𝑎+(𝑛+1)𝑑)
  • C𝑛2(𝑎+(𝑛−1)𝑑)
  • D12(2𝑎+(𝑛−1)𝑑)
  • E𝑛2(𝑎+2(𝑛−1)𝑑)

Q3:

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

  • A𝑎+𝑙
  • B𝑛2(𝑎+𝑙)
  • C12(𝑎−𝑙)
  • D𝑛2(𝑎−𝑙)
  • E12(𝑎+𝑙)

Q4:

Find, in terms of 𝑛, the sum of the arithmetic sequence (9,10,11,…,𝑛+8).

  • A𝑛2(𝑛+17)
  • B𝑛2(𝑛+8)
  • C𝑛2(𝑛+9)
  • D𝑛2(𝑛+10)
  • E𝑛(𝑛+17)

Q5:

Find the sum of the first 10 terms of the sequence 𝑎 where 𝑎=2𝑛+4.

Q6:

Find the sum of the first 17 terms of the arithmetic series 12+21+30+⋯.

Q7:

Find the least number of terms needed to make the sum of the arithmetic sequence (15,10,5,…) negative.

Q8:

In an arithmetic sequence that starts at 𝑎, 𝑎=29 and the sum of the eighth and the twelfth terms exceeds the fifteenth by 7. Find the number of terms whose sum is 322.

Q9:

Find the sum of the first 21 terms of the arithmetic sequence given 𝑎+𝑎=−232 and 𝑎=−130.

Q10:

Find the sum of the terms of the 11-term arithmetic sequence whose first term is −92 and the last term is −102.

This lesson includes 96 additional questions and 716 additional question variations for subscribers.

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