Lesson Worksheet: Finding the Arithmetic Sequence Mathematics

In this worksheet, we will practice finding arithmetic sequences given information about their terms and relationships between them.


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

  • A(66,68,70,72,74,), 𝑎=2𝑛
  • B(64,66,68,70,72,), 𝑎=2𝑛+62
  • C(62,64,66,68,70,), 𝑎=2𝑛+62
  • D(64,66,68,70,72,), 𝑎=2𝑛


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 list of these intermediate terms.

  • A(55,43,31,,209)
  • B(31,7,17,,173)
  • C(48,41,34,,92)
  • D(43,31,19,,197)
  • E(44,33,22,,176)


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

  • A(82,93,104,,236)
  • B(82,71,60,,72)
  • C(82,93,104,)
  • D(93,104,115,,247)
  • E(236,225,214,,82)


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

  • A(34,32,30,)
  • B(18,16,14,)
  • C(36,34,32,)
  • D(16,14,12,)


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(71,74,77,)
  • B(139,142,145,)
  • C(68,71,74,)
  • D(136,139,142,)


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

  • A558,7,90514,3,9997,
  • B27922,27944,0,
  • C(99,90,81,)
  • D(99,108,117,)
  • E(90,81,72,)


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(19,20,21,)
  • B(18,19,20,)
  • C(9,10,11,)
  • D(10,11,12,)


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

  • A(3,31,59,)
  • B(28,25,22,)
  • C(28,31,34,)
  • D(28,31,34,)


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

  • A(83,74,65,)
  • B(92,101,110,)
  • C4,68341,9,07382,4,39041,
  • D(92,83,74,)
  • E21,87841,22,18441,22,49041,


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

  • A13,46318,3469,
  • B(13,26,39,)
  • C(13,0,13,)
  • D(13,0,13,)
  • E(13,26,39,)

This lesson includes 15 additional questions and 225 additional question variations for subscribers.

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