Lesson Worksheet: The General Term of a Sequence Mathematics

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=𝑛14.

Q3:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=𝑛14, where 𝑛1.

  • A14,13,10,5,2
  • B13,10,5,2,11
  • C12,10,8,6,4
  • D15,18,23,30,39

Q4:

Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=5𝑛12.

  • A513,514,13,516,517
  • B514,13,516,517,518
  • C12,59,58,57,56
  • D511,12,59,58,57
  • 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(𝑛1)
  • B52+30(𝑛1)
  • C52+32(𝑛+1)
  • D52+32(𝑛1)
  • E84+30(𝑛+1)

Q6:

Find the eighth term of the sequence whose 𝑛th term is given by 𝑎=63𝑛2, where 𝑛.

  • A4724
  • B74
  • C54
  • 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 𝑛1.

  • A1,116,181,1256,1625
  • B1,132,1243,11,024,13,125
  • C1,132,1243,11,024,13,125
  • D1,116,181,1256,1625

Q9:

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

  • A(1)𝑛1
  • B(1)𝑛+1
  • C(1)𝑛1
  • D(1)𝑛+1
  • E(1)𝑛+1

Q10:

Find the first five terms of the sequence 𝑎, given 𝑎=(1)9𝑎𝑛1, and 𝑎=11.

  • A199,11,199,11,199
  • B11,199,11,199,11
  • C199,11,199,11,199
  • D11,199,11,199,11

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