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Worksheet: Finding the nth Term of an Arithmetic Sequence

In this worksheet, we will practice finding the value of the nth term in an arithmetic sequence and finding a term's order given its value.

Q1:

Find the next term in the sequence 2 8 , 3 7 , 4 6 , 5 5 , 6 4 , .

Q2:

Find the first term of an arithmetic sequence whose common difference is , where .

Q3:

Find the first term of an arithmetic sequence whose common difference is , where .

Q4:

Find the first term of an arithmetic sequence whose common difference is 8, where .

Q5:

Find the value of in an arithmetic sequence whose first term is 12, given that and .

Q6:

Find the value of in an arithmetic sequence whose first term is 41, given that and .

Q7:

Find the value of in an arithmetic sequence whose first term is 21, given that and .

Q8:

Find , given the arithmetic sequence , where .

Q9:

Find , given the arithmetic sequence , where .

Q10:

An arithmetic sequence has 11 terms. Which is the middle term?

  • A 𝑎 4
  • B 𝑎 5
  • C 𝑎 7
  • D 𝑎 6
  • E 𝑎 3

Q11:

An arithmetic sequence has 51 terms. Which is the middle term?

  • A 𝑎 2 4
  • B 𝑎 2 5
  • C 𝑎 2 7
  • D 𝑎 2 6
  • E 𝑎 2 3

Q12:

Find the common difference and first term of an arithmetic sequence given the tenth term is 25 and the fifteenth term is 40.

  • AThe common difference is 15, and the first term is 25.
  • BThe common difference is 13, and the first term is 11.
  • CThe common difference is 3, and the first term is 55.
  • DThe common difference is 3, and the first term is − 2 .
  • EThe common difference is 3, and the first term is 1.

Q13:

Find the common difference and first term of an arithmetic sequence given the tenth term is 62 and the fifteenth term is 102.

  • AThe common difference is 40, and the first term is 62.
  • BThe common difference is 1 6 4 5 , and the first term is 1 1 4 5 .
  • CThe common difference is 8, and the first term is 142.
  • DThe common difference is 8, and the first term is − 1 0 .
  • EThe common difference is 8, and the first term is − 2 .

Q14:

Find the number of terms in the arithmetic sequence ( − 4 , 2 , 8 , … , 3 9 2 ) .

Q15:

Find the number of terms in the arithmetic sequence ( − 1 3 , − 2 3 , − 3 3 , … , − 9 9 3 ) .

Q16:

Find the number of terms in the arithmetic sequence ( − 6 , − 2 , 2 , … , 3 7 0 ) .

Q17:

Find the number of positive terms in the arithmetic sequence ( 8 7 , 8 0 , 7 3 , ⋯ ) .

Q18:

Find the number of positive terms in the arithmetic sequence ( 1 3 7 , 1 3 1 , 1 2 5 , ⋯ ) .

Q19:

Find the order of the term whose value is 115 given the second term of an arithmetic sequence is , and the fifth term is 7.

  • A
  • B
  • C
  • D

Q20:

Find the order of the term whose value is 35 given the second term of an arithmetic sequence is 98, and the fifth term is 77.

  • A
  • B
  • C
  • D

Q21:

Find the order of the term − 2 in the arithmetic sequence − 1 6 , − 1 3 , − 1 2 , ⋯ .

Q22:

Find in the arithmetic sequence .

  • A
  • B
  • C
  • D

Q23:

Find in the arithmetic sequence .

  • A
  • B
  • C
  • D

Q24:

Find the tenth term from the end of the arithmetic sequence ( − 1 5 , − 2 2 , − 2 9 , … , − 2 6 0 ) .

Q25:

Find the tenth term from the end of the arithmetic sequence ( − 1 , 8 , 1 7 , … , 8 1 8 ) .

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