Worksheet: Finding the Arithmetic Sequence

In this worksheet, we will practice finding arithmetic sequences given some information about it.

Q1:

Find the arithmetic sequence in which 𝑎+𝑎=28 and 𝑎×𝑎=140.

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

Q2:

Find the arithmetic sequence given 𝑎𝑎=1,708, 𝑎𝑎𝑎𝑎=336 and all terms are positive.

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

Q3:

Find the arithmetic sequence whose ninth term is 119, and the arithmetic mean between the third and fifth terms is 69.

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

Q4:

Find the arithmetic sequence for which 𝑎=279 and 𝑎 is the additive inverse of 𝑎.

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

Q5:

Find an arithmetic sequence given 𝑎=13 and 𝑎=18𝑎.

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

Q6:

Find the arithmetic sequence in which the sum of the first and third terms equals 142, and the sum of its third and fourth terms equals 151.

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

Q7:

The first and last terms of an arithmetic sequence are 55 and 209 respectively. There are 21 terms between the first and last terms. Find the a list of these intermediate terms.

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

Q8:

Find the arithmetic sequence whose twentieth term is 28, given that the sum of its third and sixth terms is greater than its ninth term by 8.

  • A ( 1 8 , 1 9 , 2 0 , )
  • B ( 9 , 1 0 , 1 1 , )
  • C ( 1 0 , 1 1 , 1 2 , )
  • D ( 1 9 , 2 0 , 2 1 , )

Q9:

Find the arithmetic sequence in which the sum of the third and fourth terms equals -290, and 𝑎 exceeds 𝑎 by 8.

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

Q10:

Find the finite sequence 𝑎, given 𝑎=82,𝑎=203 and the twelfth-to-last term is 115.

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

Q11:

Find the arithmetic sequence given 𝑎𝑎=378,𝑎𝑎=364 and all terms are positive.

  • A ( 5 , 4 , 3 , )
  • B ( 3 6 , 3 7 , 3 8 , )
  • C ( 5 , 6 , 7 , )
  • D ( 1 , 6 , 1 1 , )
  • E ( 3 6 , 3 5 , 3 4 , )

Q12:

Find the arithmetic sequence given the sum of the second and fourth means is 198 and the seventh mean is greater than the third mean by 56.

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

Q13:

Find the value of the first negative term in an arithmetic sequence in which 𝑎𝑎=44 and 𝑎+𝑎=70.

Q14:

Determine the arithmetic sequence in which 𝑎+𝑎=500 and 𝑎+𝑎+𝑎=138.

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

Q15:

Find the arithmetic sequence whose sixth term is 96 and the ratio between the fourth and tenth terms is 2326.

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

Q16:

Find the arithmetic sequence in which the sum of the second and third terms is 13, and the sum of their squares is 97.

  • A ( 1 4 , 9 , 4 , ) or (1,4,9,)
  • B ( 4 1 , 1 6 , 9 , ) or (50,9,16,)
  • C ( 1 4 , 9 , 4 , ) or (1,4,9,)
  • D ( 8 8 , 3 5 , 4 8 , ) or (78,48,35,)

Q17:

Find the increasing arithmetic sequence given 𝑎+𝑎=56 and (𝑎)=1,444.

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

Q18:

Find the arithmetic sequence given the sum of the fifth and tenth terms is 297, and the seventh term is 4 times greater than the fourth term.

  • A 9 9 , 6 6 , 3 3 ,
  • B 1 3 2 , 9 9 , 6 6 ,
  • C 3 3 , 0 , 3 3 ,
  • D 6 6 , 3 3 , 0 ,

Q19:

Find the arithmetic sequence given the fourth term is 42 and the sum of the fifth and ninth terms is 12. Then find the order of the term whose value is 330 in this sequence.

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

Q20:

Find the arithmetic sequence given 𝑎=68 and 𝑎=62. Then find the order and the value of the first term that exceeds 64.

  • A ( 7 7 , 7 4 , 7 1 , ) , 𝑎 , 67
  • B ( 1 5 7 , 1 5 4 , 1 5 1 , ) , 𝑎 , 8 8
  • C ( 8 0 , 7 7 , 7 4 , ) , 𝑎 , 67
  • D ( 1 6 0 , 1 5 7 , 1 5 4 , ) , 𝑎 , 9 1

Q21:

Find the sequence and its general term of all the even numbers greater than 62.

  • A ( 6 2 , 6 4 , 6 6 , 6 8 , 7 0 , ) , 𝑎 = 2 𝑛 + 6 2
  • B ( 6 4 , 6 6 , 6 8 , 7 0 , 7 2 , ) , 𝑎 = 2 𝑛 + 6 2
  • C ( 6 6 , 6 8 , 7 0 , 7 2 , 7 4 , ) , 𝑎 = 2 𝑛
  • D ( 6 4 , 6 6 , 6 8 , 7 0 , 7 2 , ) , 𝑎 = 2 𝑛

Q22:

Find the arithmetic sequence in which 𝑎=2𝑎+44 and the arithmetic mean of the third and sixth terms is 35.

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

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