Lesson Worksheet: The General Term of a Sequence Mathematics

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In this worksheet, we will practice using the general term or a recursive formula of a sequence to work out terms in the sequence.

Q1:

Find the next term in the sequence −8,16,−24,32,.

Q2:

Find the seventh term of the sequence 𝑎=𝑛−14.

Q3:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=𝑛−14, where 𝑛≥1.

  • A−14,−13,−10,−5,2
  • B−13,−10,−5,2,11
  • C−12,−10,−8,−6,−4
  • D15,18,23,30,39

Q4:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=5𝑛−12.

  • A513,514,13,516,517
  • B514,13,516,517,518
  • C−12,−59,−58,−57,−56
  • D−511,−12,−59,−58,−57
  • E5,52,53,54,1

Q5:

Which of the following is an expression for the general term of the sequence 52,84,116,148?

  • A84+32(𝑛−1)
  • B52+30(𝑛−1)
  • C52+32(𝑛+1)
  • D52+32(𝑛−1)
  • E84+30(𝑛+1)

Q6:

Find the eighth term of the sequence whose 𝑛th term is given by 𝑎=63𝑛−2, where 𝑛∈ℤ.

  • A−4724
  • B−74
  • C−54
  • D14

Q7:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=5𝑛+𝑛.

  • A4,12,18,16,0
  • B9,12,3,−24,−75
  • C6,28,72,144,250
  • D11,28,57,104,175

Q8:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=(−1)𝑛, where 𝑛≥1.

  • A−1,−116,−181,−1256,−1625
  • B1,−132,1243,−11,024,13,125
  • C−1,132,−1243,11,024,−13,125
  • D1,116,181,1256,1625

Q9:

Which of the following represents the general term of the sequence 2,−5,10,−17,…?

  • A(−1)𝑛−1
  • B(−1)𝑛+1
  • C(−1)𝑛−1
  • D(−1)𝑛+1
  • E(−1)𝑛+1

Q10:

Find the first five terms of the sequence 𝑎, given 𝑎=(−1)9𝑎,  𝑛≥1, and 𝑎=−11.

  • A−199,−11,199,11,−199
  • B11,−199,−11,199,11
  • C199,11,−199,−11,199
  • D−11,199,11,−199,−11

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