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Lesson: Finding the Arithmetic Sequence

Worksheet • 25 Questions

Q1:

Find the arithmetic sequence in which 𝑇 + 𝑇 = βˆ’ 2 8 2 4 and 𝑇 Γ— 𝑇 = 1 4 0 3 5 .

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

Q2:

Find the 7-term arithmetic sequence whose middle term is βˆ’ 1 0 5 and sum of the last 3 terms is βˆ’ 3 6 9 .

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

Q3:

Find the four numbers which form an arithmetic sequence given that the sum of the four terms equals 362, and the sum of the squares of the first and fourth terms exceeds the sum of the squares of the second and third terms by 900.

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

Q4:

Find the five numbers that make an increasing arithmetic sequence, given their sum is βˆ’ 5 0 and the squares of the smallest and largest terms add up to 1 000.

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

Q5:

Find the three consecutive terms of an arithmetic sequence given their sum is 243, and if βˆ’ 3 6 is added to their second term, the multiplicative inverse of the three terms will form another arithmetic sequence.

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

Q6:

Find the arithmetic sequence given 𝑇 𝑇 = 1 7 0 8 1 1 2 , 𝑇 𝑇 βˆ’ 𝑇 𝑇 = 3 3 6 6 3 1 7 2 6 and all terms are positive.

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

Q7:

Find the arithmetic sequence whose ninth term is βˆ’ 1 1 9 , and the arithmetic mean between the third and fifth terms is βˆ’ 6 9 .

  • A ( βˆ’ 3 9 , βˆ’ 4 9 , βˆ’ 5 9 , … )
  • B ο€Ό βˆ’ 1 9 , βˆ’ 6 3 2 , βˆ’ 4 4 , … 
  • C ( βˆ’ 1 0 , βˆ’ 4 9 , βˆ’ 8 8 , … )
  • D ( βˆ’ 3 9 , βˆ’ 2 9 , βˆ’ 1 9 , … )
  • E ( βˆ’ 4 9 , βˆ’ 5 9 , βˆ’ 6 9 , … )

Q8:

Find the four numbers which form an arithmetic sequence given that the sum of the four terms equals βˆ’ 1 1 6 and the sum of the squares of the four terms equals 3 444.

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

Q9:

Find the arithmetic sequence for which 𝑇 = 2 7 9 4 3 and 𝑇 1 1 is the additive inverse of 𝑇 1 3 .

  • A ( βˆ’ 9 9 , βˆ’ 9 0 , βˆ’ 8 1 , … )
  • B ο€Ό 2 7 9 2 2 , 2 7 9 4 4 , 0 , … 
  • C ( βˆ’ 9 0 , βˆ’ 8 1 , βˆ’ 7 2 , … )
  • D ο€Ό 5 5 8 , 7 9 0 5 1 4 , 3 9 9 9 7 , β‹― 
  • E ( βˆ’ 9 9 , βˆ’ 1 0 8 , βˆ’ 1 1 7 , … )

Q10:

Find an arithmetic sequence given 𝑇 = 1 3 1 and 𝑇 = 1 8 𝑇 1 8 𝑛 𝑛 .

  • A ( 1 3 , 2 6 , 3 9 , … )
  • B ( βˆ’ 1 3 , βˆ’ 2 6 , βˆ’ 3 9 , … )
  • C ( 1 3 , 0 , βˆ’ 1 3 , … )
  • D ο€Ό 1 3 , 4 6 3 1 8 , 3 4 6 9 , β‹― 
  • E ( βˆ’ 1 3 , 0 , 1 3 , … )

Q11:

Find the arithmetic sequence in which the sum of the first and third terms equals βˆ’ 1 4 2 , and the sum of its third and fourth terms equals βˆ’ 1 5 1 .

  • A ( βˆ’ 6 8 , βˆ’ 7 1 , βˆ’ 7 4 , β‹― )
  • B ( βˆ’ 7 1 , βˆ’ 7 4 , βˆ’ 7 7 , β‹― )
  • C ( βˆ’ 1 3 9 , βˆ’ 1 4 2 , βˆ’ 1 4 5 , β‹― )
  • D ( βˆ’ 1 3 6 , βˆ’ 1 3 9 , βˆ’ 1 4 2 , β‹― )

Q12:

The first and last terms of an arithmetic sequence are βˆ’ 5 5 and 209 respectively. There are 21 terms between the first and last terms. Find the a list of these intermediate terms.

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

Q13:

What is the next number in the sequence √ 6 , √ 2 4 , √ 5 4 , √ 9 6 ?

  • A √ 1 5 0
  • B √ 1 3 8
  • C √ 1 8 0
  • D √ 1 2 0

Q14:

Find the three numbers which form an arithmetic sequence given the sum is 69 and product is 6 279.

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

Q15:

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 ( 9 , 1 0 , 1 1 , β‹― )
  • B ( 1 0 , 1 1 , 1 2 , β‹― )
  • C ( 1 9 , 2 0 , 2 1 , β‹― )
  • D ( 1 8 , 1 9 , 2 0 , β‹― )

Q16:

Find the arithmetic sequence in which the sum of the third and fourth terms equals -290, and 𝑇 9 exceeds 𝑇 5 by 8.

  • A ( βˆ’ 1 5 0 , βˆ’ 1 4 8 , βˆ’ 1 4 6 , β‹― )
  • B ( βˆ’ 1 4 8 , βˆ’ 1 4 6 , βˆ’ 1 4 4 , β‹― )
  • C ( βˆ’ 2 9 8 , βˆ’ 2 9 6 , βˆ’ 2 9 4 , β‹― )
  • D ( βˆ’ 3 0 0 , βˆ’ 2 9 8 , βˆ’ 2 9 6 , β‹― )

Q17:

Find the finite sequence 𝑇 𝑛 , given 𝑇 = βˆ’ 8 2 , 𝑇 = βˆ’ 2 0 3 1 1 2 and the twelfth-to-last term is βˆ’ 1 1 5 .

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

Q18:

Find the arithmetic sequence given 𝑇 𝑇 = 3 7 8 , 𝑇 𝑇 = 3 6 4 2 3 1 0 9 2 4 and all terms are positive.

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

Q19:

Find the arithmetic sequence starting at 𝑇 1 in which 𝑇 = 1 6 9 1 3 , and the ratio of the sum of its first five terms to the sum of the following five terms is 7 9 1 2 4 .

  • A ( 6 1 , 7 0 , 7 9 , … )
  • B ( 6 1 , 1 6 9 , 2 7 7 , … )
  • C ( 9 , 7 0 , 1 3 1 , … )
  • D ο€Ό 6 7 6 9 , 2 4 7 3 , 8 0 6 9 , β‹― 
  • E ο€Ό 1 2 2 , 1 5 1 1 1 2 , 7 7 9 6 , β‹― 

Q20:

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

Q21:

Find the value of the first negative term in an arithmetic sequence in which 𝑇 βˆ’ 𝑇 = 4 4 2 7 4 9 and 𝑇 + 𝑇 = 7 0 2 3 3 .

Q22:

Find the four numbers which form an arithmetic sequence given that the sum of the four terms equals βˆ’ 1 6 0 and when 7 is added to the second number, the first, second, and fourth numbers form another arithmetic sequence.

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

Q23:

Find the first three terms in the sequence which has general term π‘Ž = 1 7 + 1 4 𝑛 𝑛 and 𝑛 β‰₯ 1 . Then find the order of the term whose value is 157 and the order of the first term whose value is more than 100.

  • A 3 1 , 4 5 , 5 9 , π‘Ž 1 0 , π‘Ž 6
  • B 3 1 , 4 5 , 5 9 , π‘Ž 9 , π‘Ž 5
  • C 4 5 , 5 9 , 7 3 , π‘Ž 1 1 , π‘Ž 5
  • D 4 5 , 5 9 , 7 3 , π‘Ž 1 0 , π‘Ž 6

Q24:

Determine the arithmetic sequence in which 𝑇 + 𝑇 = 5 0 0 5 0 2 8 and 𝑇 + 𝑇 + 𝑇 = 1 3 8 3 1 1 3 5 .

  • A ( βˆ’ 9 2 , βˆ’ 8 3 , βˆ’ 7 4 , … )
  • B ο€Ό 2 1 8 7 8 4 1 , 2 2 1 8 4 4 1 , 2 2 4 9 0 4 1 , β‹― 
  • C ( βˆ’ 8 3 , βˆ’ 7 4 , βˆ’ 6 5 , … )
  • D ο€Ό 4 6 8 3 4 1 , 9 0 7 3 8 2 , 4 3 9 0 4 1 , β‹― 
  • E ( βˆ’ 9 2 , βˆ’ 1 0 1 , βˆ’ 1 1 0 , … )

Q25:

Find the arithmetic sequence whose sixth term is 96 and the ratio between the fourth and tenth terms is 2 3 2 6 .

  • A ( 8 6 , 8 8 , 9 0 , 9 2 , … )
  • B ο€Ό 9 6 , 2 5 1 9 2 6 , 1 2 7 1 1 3 , 2 5 6 5 2 6 , β‹― 
  • C ( 2 , 8 8 , 1 7 4 , 2 6 0 , … )
  • D ( 4 6 , 5 6 , 6 6 , 7 6 , … )
  • E ( 8 8 , 9 0 , 9 2 , 9 4 , … )
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