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 𝑛th term is given by π‘Ž=ο€Ό11𝑛6πœ‹οˆοŠcos where 𝑛β‰₯1.

  • Aβˆ’βˆš32,12,0,βˆ’12,√32
  • B√32,12,1,βˆ’12,βˆ’βˆš32
  • Cβˆ’βˆš32,βˆ’12,0,12,√32
  • D√32,12,0,βˆ’12,βˆ’βˆš32

Q2:

Which of the following are the first five term of the sequence with general term π‘Ž=βˆ’99βˆ’17βˆšπ‘›οŠ and 𝑛β‰₯1?

  • Aβˆ’82,βˆ’1812,βˆ’2803,βˆ’3794,βˆ’4785,…
  • Bβˆ’116,βˆ’99βˆ’17√22,βˆ’99βˆ’17√33,βˆ’2152,βˆ’99βˆ’17√55,…
  • Cβˆ’116,βˆ’99+17√22,βˆ’99+17√33,βˆ’2152,βˆ’99+17√55,…
  • Dβˆ’116,βˆ’2152,βˆ’3143,βˆ’4134,βˆ’5125,…

Q3:

Find the first five terms of the sequence whose general term is given by π‘Ž=𝑛(π‘›βˆ’34), where 𝑛β‰₯1.

  • A(βˆ’33,βˆ’32,βˆ’31,βˆ’30,βˆ’29)
  • B(33,64,93,120,145)
  • C(33,32,31,30,29)
  • D(βˆ’33,βˆ’64,βˆ’93,βˆ’120,βˆ’145)

Q4:

Find the first five terms of the sequence with general term π‘Ž=37, where 𝑛β‰₯1.

  • A(37,74,111,148,185)
  • B(38,39,40,41,42)
  • C(36,35,34,33,32)
  • D(37,37,37,37,37)

Q5:

Find the seventh term of the sequence π‘Ž=π‘›βˆ’14.

Q6:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=5𝑛+π‘›οŠοŠ¨οŠ©.

  • A4,12,18,16,0
  • B9,12,3,βˆ’24,βˆ’75
  • C6,28,72,144,250
  • D11,28,57,104,175

Q7:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=(βˆ’1)π‘›οŠοŠοŠ«, where 𝑛β‰₯1.

  • Aο€Όβˆ’1,βˆ’116,βˆ’181,βˆ’1256,βˆ’1625
  • Bο€Ό1,βˆ’132,1243,βˆ’11,024,13,125
  • Cο€Όβˆ’1,132,βˆ’1243,11,024,βˆ’13,125
  • Dο€Ό1,116,181,1256,1625

Q8:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=π‘›βˆ’14, where 𝑛β‰₯1.

  • A(βˆ’14,βˆ’13,βˆ’10,βˆ’5,2)
  • B(βˆ’13,βˆ’10,βˆ’5,2,11)
  • C(βˆ’12,βˆ’10,βˆ’8,βˆ’6,βˆ’4)
  • D(15,18,23,30,39)

Q9:

Find the eighth term of the sequence whose 𝑛th term is given by π‘Ž=63π‘›βˆ’2, where π‘›βˆˆβ„€οŠ°.

  • Aβˆ’4724
  • Bβˆ’74
  • Cβˆ’54
  • D14

Q10:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=(βˆ’2)βˆ’5π‘›βˆ’91.

  • Aο€Ό143,481,219,1671,1633,β‹―οˆ
  • Bο€Όβˆ’143,481,βˆ’219,1671,βˆ’1633,β‹―οˆ
  • Cο€Ό148,4101,353,8111,558,β‹―οˆ
  • Dο€Ό148,βˆ’4101,453,βˆ’16111,829,β‹―οˆ
  • Eο€Όβˆ’191,148,βˆ’4101,453,βˆ’16111,β‹―οˆ

Q11:

Find the fourth term of the sequence with general term π‘Ž=βˆšπ‘›βˆ’10𝑛+39, where 𝑛β‰₯1.

  • Aβˆ’279
  • B243
  • Cβˆ’2
  • Dβˆ’4
  • Eβˆ’479

Q12:

Find the first five terms of the sequence whose general term is given by π‘Ž=(βˆ’1)(π‘›βˆ’9), where 𝑛β‰₯1.

  • A(64,βˆ’49,36,βˆ’25,16)
  • B(81,βˆ’64,49,βˆ’36,25)
  • C(βˆ’64,49,βˆ’36,25,βˆ’16)
  • D(βˆ’100,121,βˆ’144,169,βˆ’196)

Q13:

Find the fifth term of the sequence π‘Ž=(βˆ’1)57π‘›οŠοŠ.

  • Aβˆ’1171
  • Bβˆ’1285
  • C1285
  • D1570

Q14:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=5π‘›βˆ’12.

  • Aο€Ό513,514,13,516,517
  • Bο€Ό514,13,516,517,518
  • Cο€Όβˆ’12,βˆ’59,βˆ’58,βˆ’57,βˆ’56
  • Dο€Όβˆ’511,βˆ’12,βˆ’59,βˆ’58,βˆ’57
  • Eο€Ό5,52,53,54,1

Q15:

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž=ο€Ό7𝑛6πœ‹οˆοŠsin where 𝑛β‰₯1.

  • Aο€Ώ12,βˆ’βˆš32,βˆ’1,βˆ’βˆš32,12
  • Bο€Ώβˆ’12,√32,1,√32,βˆ’12
  • Cο€Ώ12,βˆ’βˆš32,1,βˆ’βˆš32,12
  • Dο€Ώβˆ’12,√32,βˆ’1,√32,βˆ’12

Q16:

Find the first five terms of the sequence π‘ŽοŠ, given π‘Ž=(βˆ’1)9π‘ŽοŠοŠ°οŠ§οŠοŠ, 𝑛β‰₯1, and π‘Ž=βˆ’11.

  • Aο€Όβˆ’199,βˆ’11,199,11,βˆ’199
  • Bο€Ό11,βˆ’199,βˆ’11,199,11
  • Cο€Ό199,11,βˆ’199,βˆ’11,199
  • Dο€Όβˆ’11,199,11,βˆ’199,βˆ’11

Q17:

Is the sequence π‘Ž=(βˆ’1)11π‘›βˆ’22 increasing, decreasing, or neither?

  • Aπ‘ŽοŠ is decreasing.
  • Bπ‘ŽοŠ is increasing.
  • Cπ‘ŽοŠ is neither increasing nor decreasing.

Q18:

Find, in terms of 𝑛, the general term of the sequence ((168Γ—169),(169Γ—170),(170Γ—171),(171Γ—172),…).

  • A(𝑛+167)(𝑛+168)
  • B168𝑛(𝑛+167)
  • C(π‘›βˆ’167)(𝑛+167)
  • D𝑛(𝑛+167)

Q19:

Find, in terms of 𝑛, the general term of the sequence 6388,6489,6590,6691,….

  • A𝑛+63𝑛+88
  • B2𝑛+612𝑛+86
  • C𝑛+87𝑛+62
  • D𝑛+62𝑛+87

Q20:

Find, in terms of 𝑛, the general term of the sequence βˆ’2,2,βˆ’83,4,….

  • A(βˆ’2)βˆ’1
  • B(βˆ’2)π‘›οŠ
  • Cβˆ’2π‘›βˆ’1
  • D(βˆ’2)

Q21:

Find, in terms of 𝑛, the general term of the sequence 350+12,350+13,350+14,350+15,….

  • A350+(βˆ’1)𝑛+1
  • B350+1𝑛+1
  • C350+1𝑛
  • D350+(βˆ’1)𝑛+1

Q22:

Find, in terms of 𝑛, the general term of the sequence (9,72,243,576,…).

  • A𝑛+9
  • B𝑛(𝑛+9)
  • C9(π‘›βˆ’9)
  • D9π‘›οŠ©

Q23:

Find, in terms of 𝑛, the general term of the sequence (18,72,162,288,…).

  • A19π‘›βˆ’1
  • B18π‘›οŠ©
  • C17𝑛+1
  • D18π‘›οŠ¨
  • E18𝑛

Q24:

Find, in terms of 𝑛, the general term of the sequence coscoscoscos2πœ‹,4πœ‹,6πœ‹,8πœ‹,….

  • Acos(2π‘›πœ‹)
  • Bcos(2(𝑛+1)πœ‹)
  • Ccos(4π‘›πœ‹)
  • Dcos(2(π‘›βˆ’1)πœ‹)

Q25:

The sequence π‘ŽοŠ, where 𝑛β‰₯1, is given by 0,1,βˆ’1,βˆ’2,2,3,βˆ’3,βˆ’4,4,5….

List the next 6 terms π‘Ž,…,π‘ŽοŠ§οŠ§οŠ§οŠ¬.

  • Aπ‘Ž=βˆ’5, π‘Ž=6, π‘Ž=6, π‘Ž=βˆ’7οŠͺ, π‘Ž=βˆ’7, π‘Ž=8
  • Bπ‘Ž=5, π‘Ž=6, π‘Ž=βˆ’6, π‘Ž=βˆ’7οŠͺ, π‘Ž=7, π‘Ž=8
  • Cπ‘Ž=βˆ’6, π‘Ž=6, π‘Ž=βˆ’7, π‘Ž=7οŠͺ, π‘Ž=7, π‘Ž=8
  • Dπ‘Ž=6, π‘Ž=βˆ’6, π‘Ž=βˆ’6, π‘Ž=7οŠͺ, π‘Ž=7, π‘Ž=βˆ’8
  • Eπ‘Ž=βˆ’5, π‘Ž=βˆ’6, π‘Ž=6, π‘Ž=7οŠͺ, π‘Ž=βˆ’7, π‘Ž=βˆ’8

By listing the elements π‘Ž,π‘Ž,π‘Ž,π‘Ž,β€¦οŠ§οŠ«οŠ―οŠ§οŠ©, give a formula for π‘ŽοŠͺ, in terms of 𝑛, for 𝑛β‰₯1.

  • Aπ‘Ž=(𝑛+1)οŠͺ
  • Bπ‘Ž=2(𝑛+1)οŠͺ
  • Cπ‘Ž=(π‘›βˆ’1)οŠͺ
  • Dπ‘Ž=(2π‘›βˆ’1)οŠͺ
  • Eπ‘Ž=2(π‘›βˆ’1)οŠͺ

Give a formula for π‘ŽοŠͺ, in terms of 𝑛, for 𝑛β‰₯1.

  • Aπ‘Ž=2(π‘›βˆ’1)οŠͺ
  • Bπ‘Ž=2𝑛+1οŠͺ
  • Cπ‘Ž=2π‘›βˆ’1οŠͺ
  • Dπ‘Ž=2(𝑛+1)οŠͺ
  • Eπ‘Ž=𝑛+1οŠͺ

Give a formula for π‘ŽοŠͺ, in terms of 𝑛, for 𝑛β‰₯1.

  • Aπ‘Ž=1βˆ’π‘›οŠͺ
  • Bπ‘Ž=1+2𝑛οŠͺ
  • Cπ‘Ž=1βˆ’2𝑛οŠͺ
  • Dπ‘Ž=2+𝑛οŠͺ
  • Eπ‘Ž=2βˆ’π‘›οŠͺ

Give a formula for π‘ŽοŠͺ, in terms of 𝑛, for 𝑛β‰₯1.

  • Aπ‘Ž=2𝑛οŠͺ
  • Bπ‘Ž=βˆ’2𝑛οŠͺ
  • Cπ‘Ž=1+2𝑛οŠͺ
  • Dπ‘Ž=1βˆ’2𝑛οŠͺ
  • Eπ‘Ž=2βˆ’π‘›οŠͺ

What is π‘ŽοŠ§οŠ¨οŽ•οŠ©οŠͺ?

  • Aπ‘Ž=6,172οŠ§οŠ¨οŽ•οŠ©οŠͺ
  • Bπ‘Ž=6,170οŠ§οŠ¨οŽ•οŠ©οŠͺ
  • Cπ‘Ž=6,710οŠ§οŠ¨οŽ•οŠ©οŠͺ
  • Dπ‘Ž=βˆ’6,172οŠ§οŠ¨οŽ•οŠ©οŠͺ
  • Eπ‘Ž=βˆ’6,170οŠ§οŠ¨οŽ•οŠ©οŠͺ

Solve π‘Ž=17 for 𝑛.

  • A𝑛=32
  • B𝑛=34
  • C𝑛=33
  • D𝑛=35
  • E𝑛=37

What is the range of the function π‘ŽοŠ?

  • AThe set of positive integers
  • BThe set of all integers
  • CThe set of negative rationals
  • DThe set of postive rationals
  • EThe set of negative integers

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