Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Homework Help

Lesson: Finding the nth Term of an Arithmetic Sequence

In this lesson, we will learn how to find the value of the nth term in an arithmetic sequence and how to find a term's order given its value.

Sample Question Videos

01:28

Worksheet • 25 Questions • 1 Video

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

Q11:

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

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

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

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

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 ) .
Preview

Related Lessons

Related Videos

Related Worksheets