Worksheet: Finding the Terms of a Sequence Given Its General Term

In this worksheet, we will practice finding the terms of a sequence given its general term.

Q1:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = 1 1 𝑛 6 𝜋 c o s where 𝑛 1 .

  • A 3 2 , 1 2 , 0 , 1 2 , 3 2
  • B 3 2 , 1 2 , 0 , 1 2 , 3 2
  • C 3 2 , 1 2 , 0 , 1 2 , 3 2
  • D 3 2 , 1 2 , 1 , 1 2 , 3 2

Q2:

Which of the following are the first five term of the sequence with general term 𝑎 = 9 9 1 7 𝑛 and 𝑛 1 ?

  • A 1 1 6 , 9 9 1 7 2 2 , 9 9 1 7 3 3 , 2 1 5 2 , 9 9 1 7 5 5 ,
  • B 1 1 6 , 2 1 5 2 , 3 1 4 3 , 4 1 3 4 , 5 1 2 5 ,
  • C 8 2 , 1 8 1 2 , 2 8 0 3 , 3 7 9 4 , 4 7 8 5 ,
  • D 1 1 6 , 9 9 + 1 7 2 2 , 9 9 + 1 7 3 3 , 2 1 5 2 , 9 9 + 1 7 5 5 ,

Q3:

Find the first five terms of the sequence whose general term is given by 𝑎 = 𝑛 ( 𝑛 3 4 ) , where 𝑛 1 .

  • A ( 3 3 , 6 4 , 9 3 , 1 2 0 , 1 4 5 )
  • B ( 3 3 , 3 2 , 3 1 , 3 0 , 2 9 )
  • C ( 3 3 , 3 2 , 3 1 , 3 0 , 2 9 )
  • D ( 3 3 , 6 4 , 9 3 , 1 2 0 , 1 4 5 )

Q4:

Find the first five terms of the sequence with general term 𝑎 = 3 7 , where 𝑛 1 .

  • A ( 3 6 , 3 5 , 3 4 , 3 3 , 3 2 )
  • B ( 3 7 , 3 7 , 3 7 , 3 7 , 3 7 )
  • C ( 3 8 , 3 9 , 4 0 , 4 1 , 4 2 )
  • D ( 3 7 , 7 4 , 1 1 1 , 1 4 8 , 1 8 5 )

Q5:

Find the seventh term of the sequence 𝑎 = 𝑛 1 4 .

Q6:

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

  • A 4 , 1 2 , 1 8 , 1 6 , 0
  • B 1 1 , 2 8 , 5 7 , 1 0 4 , 1 7 5
  • C 6 , 2 8 , 7 2 , 1 4 4 , 2 5 0
  • D 9 , 1 2 , 3 , 2 4 , 7 5

Q7:

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

  • A 1 , 1 3 2 , 1 2 4 3 , 1 1 , 0 2 4 , 1 3 , 1 2 5
  • B 1 , 1 1 6 , 1 8 1 , 1 2 5 6 , 1 6 2 5
  • C 1 , 1 3 2 , 1 2 4 3 , 1 1 , 0 2 4 , 1 3 , 1 2 5
  • D 1 , 1 1 6 , 1 8 1 , 1 2 5 6 , 1 6 2 5

Q8:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = 1 9 𝑛 + 2 , where 𝑛 1 .

  • A ( 2 1 , 4 0 , 5 9 , 7 8 , 9 7 )
  • B ( 1 7 , 3 6 , 5 5 , 7 4 , 9 3 )
  • C ( 2 1 , 4 0 , 5 9 , 7 8 , 9 7 )
  • D ( 1 7 , 3 6 , 5 5 , 7 4 , 9 3 )

Q9:

Find the first five terms of the sequence whose 𝑛 th term is given by 𝑎 = 𝑛 1 4 , where 𝑛 1 .

  • A ( 1 2 , 1 0 , 8 , 6 , 4 )
  • B ( 1 4 , 1 3 , 1 0 , 5 , 2 )
  • C ( 1 3 , 1 0 , 5 , 2 , 1 1 )
  • D ( 1 5 , 1 8 , 2 3 , 3 0 , 3 9 )

Q10:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = 3 8 × 1 5 , where 𝑛 1 .

  • A 3 8 5 , 3 8 2 5 , 3 8 1 2 5 , 3 8 6 2 5 , 3 8 3 , 1 2 5
  • B 3 8 5 , 3 8 2 5 , 3 8 1 2 5 , 3 8 6 2 5 , 3 8 3 , 1 2 5
  • C 1 5 , 1 2 5 , 1 1 2 5 , 1 6 2 5 , 1 3 , 1 2 5
  • D 1 5 , 1 2 5 , 1 1 2 5 , 1 6 2 5 , 1 3 , 1 2 5

Q11:

Find the eighth term of the sequence whose 𝑛 t h term is given by 𝑎 = 6 3 𝑛 2 , where 𝑛 .

  • A 7 4
  • B 1 4
  • C 4 7 2 4
  • D 5 4

Q12:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = ( 2 ) 5 𝑛 9 1 .

  • A 1 4 8 , 4 1 0 1 , 4 5 3 , 1 6 1 1 1 , 8 2 9 ,
  • B 1 4 3 , 4 8 1 , 2 1 9 , 1 6 7 1 , 1 6 3 3 ,
  • C 1 9 1 , 1 4 8 , 4 1 0 1 , 4 5 3 , 1 6 1 1 1 ,
  • D 1 4 8 , 4 1 0 1 , 3 5 3 , 8 1 1 1 , 5 5 8 ,
  • E 1 4 3 , 4 8 1 , 2 1 9 , 1 6 7 1 , 1 6 3 3 ,

Q13:

Find the fourth term of the sequence with general term 𝑎 = 𝑛 1 0 𝑛 + 3 9 , where 𝑛 1 .

  • A 2 7 9
  • B 4
  • C 2 4 3
  • D 2
  • E 4 7 9

Q14:

Find the third term, 𝑎 , of the sequence 𝑎 = 5 𝑛 + 8 .

Q15:

Find the first five terms of the sequence whose general term is given by 𝑎 = ( 1 ) ( 𝑛 9 ) , where 𝑛 1 .

  • A ( 6 4 , 4 9 , 3 6 , 2 5 , 1 6 )
  • B ( 8 1 , 6 4 , 4 9 , 3 6 , 2 5 )
  • C ( 1 0 0 , 1 2 1 , 1 4 4 , 1 6 9 , 1 9 6 )
  • D ( 6 4 , 4 9 , 3 6 , 2 5 , 1 6 )

Q16:

Find the fifth term of the sequence 𝑎 = ( 1 ) 5 7 𝑛 .

  • A 1 2 8 5
  • B 1 5 7 0
  • C 1 2 8 5
  • D 1 1 7 1

Q17:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = 5 𝑛 1 2 .

  • A 5 1 3 , 5 1 4 , 1 3 , 5 1 6 , 5 1 7
  • B 5 1 4 , 1 3 , 5 1 6 , 5 1 7 , 5 1 8
  • C 1 2 , 5 9 , 5 8 , 5 7 , 5 6
  • D 5 1 1 , 1 2 , 5 9 , 5 8 , 5 7
  • E 5 , 5 2 , 5 3 , 5 4 , 1

Q18:

Find the first five terms of the sequence whose 𝑛 t h term is given by 5 .

  • A ( 5 , 2 5 , 1 2 5 , 6 2 5 , 3 , 1 2 5 )
  • B ( 5 , 2 5 , 1 2 5 , 6 2 5 , 3 , 1 2 5 )
  • C ( 5 , 1 0 , 1 5 , 2 0 , 2 5 )
  • D ( 5 , 1 0 , 1 5 , 2 0 , 2 5 )

Q19:

Find the first five terms of the sequence whose 𝑛 t h term is given by 𝑎 = 7 𝑛 6 𝜋 s i n where 𝑛 1 .

  • A 1 2 , 3 2 , 1 , 3 2 , 1 2
  • B 1 2 , 3 2 , 1 , 3 2 , 1 2
  • C 1 2 , 3 2 , 1 , 3 2 , 1 2
  • D 1 2 , 3 2 , 1 , 3 2 , 1 2

Q20:

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

  • A 1 1 , 1 9 9 , 1 1 , 1 9 9 , 1 1
  • B 1 1 , 1 9 9 , 1 1 , 1 9 9 , 1 1
  • C 1 9 9 , 1 1 , 1 9 9 , 1 1 , 1 9 9
  • D 1 9 9 , 1 1 , 1 9 9 , 1 1 , 1 9 9

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