Lesson Worksheet: Finding the 𝑛th Term of a Geometric Sequence Mathematics • 9th Grade

In this worksheet, we will practice writing explicit and recursive formulas for geometric sequences to find the value of the 𝑛th term in a geometric sequence and finding a term’s order given its value.


Find the value of the second term of the geometric sequence π‘Ž=16Γ—2, where 𝑛β‰₯1.

  • A83
  • B13,888
  • C163
  • D323


The recursive formula for a geometric sequence is π‘Ž=0.345π‘ŽοŠοŠ°οŠ§οŠ and π‘Ž=9.8 for 𝑛β‰₯1. Give an explicit formula for the sequence.

  • Aπ‘Ž=9.8(0.345) for 𝑛>0
  • Bπ‘Ž=9.8βˆ’6.419(π‘›βˆ’1) for 𝑛β‰₯0
  • Cπ‘Ž=9.8(0.345) for 𝑛β‰₯0
  • Dπ‘Ž=9.8(2.899) for 𝑛β‰₯0
  • Eπ‘Ž=3.38π‘ŸοŠοŠοŠ±οŠ¨ for 𝑛β‰₯0


Find a formula for the general term of the geometric sequence 3,15,75,375,1,875,….

  • Aπ‘Ž=5Γ—(3)
  • Bπ‘Ž=5Γ—(3)
  • Cπ‘Ž=3Γ—(5)
  • Dπ‘Ž=3Γ—(5)
  • Eπ‘Ž=3Γ—(5)


Find, in terms of 𝑛, the general term of the geometric sequence βˆ’76,βˆ’38,βˆ’19,βˆ’192,….

  • Aβˆ’76Γ—2
  • Bβˆ’76Γ—ο€Ό12
  • Cβˆ’76Γ—2
  • Dβˆ’76Γ—ο€Ό12


Find, in terms of 𝑛, the general term of the sequence ο€Ό1,19,181,1729.

  • A19()
  • B19βˆ’1
  • C19()
  • D19


Find the first three terms of a geometric sequence given π‘Ž=βˆ’3,616 and the common ratio is βˆ’2.

  • A1113,βˆ’2113,4113
  • B113,226,452
  • C113,βˆ’226,452
  • D113,βˆ’1132,1134
  • E113,1132,1134


Find the three consecutive numbers of a geometric sequence, given that the sum of the terms is βˆ’14 and the product is 216.

  • Aβˆ’2, 6, βˆ’18
  • B16, βˆ’118, 154
  • Cβˆ’12, 16, βˆ’118
  • D6, βˆ’18, 54
  • E6, βˆ’2, 23


Find the order of the term whose value is 4,374 in the geometric sequence π‘Ž=23(3).


Find the number of terms of the geometric sequence ο€Ό112,56,28,…,74.


Find the order of the term 1639 in the geometric sequence 1156,βˆ’178,139,….

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