Lesson Worksheet: Arithmetic Series Mathematics • 10th Grade

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 π‘Ž and whose common difference is 𝑑.

  • A𝑛2(2π‘Ž+(π‘›βˆ’1)𝑑)
  • B𝑛2(2π‘Ž+(𝑛+1)𝑑)
  • C𝑛2(π‘Ž+(π‘›βˆ’1)𝑑)
  • D12(2π‘Ž+(π‘›βˆ’1)𝑑)
  • E𝑛2(π‘Ž+2(π‘›βˆ’1)𝑑)

Q3:

Write an expression for the sum of the first 𝑛 terms of an arithmetic sequence with first term π‘Ž and last term 𝑙.

  • Aπ‘Ž+𝑙
  • B𝑛2(π‘Ž+𝑙)
  • C12(π‘Žβˆ’π‘™)
  • D𝑛2(π‘Žβˆ’π‘™)
  • E12(π‘Ž+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 π‘ŽοŠ where π‘Ž=2𝑛+4.

Q6:

Find the sum of the first 17 terms of the arithmetic series 12+21+30+β‹―.

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 π‘ŽοŠ§, π‘Ž=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 π‘Ž+π‘Ž=βˆ’232οŠͺ and π‘Ž=βˆ’130.

Q10:

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

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

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