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

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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.

Q1:

Find the value of the second term of the geometric sequence 𝑎=16×2, where 𝑛≥1.

  • A83
  • B13,888
  • C163
  • D323

Q2:

The recursive formula for a geometric sequence is 𝑢=0.345𝑢 and 𝑢=9.8 for 𝑛≥1. Give an explicit formula for the sequence.

  • A𝑢=9.8(0.345) for 𝑛>1
  • B𝑢=9.8−6.419(𝑛−1) for 𝑛≥1
  • C𝑢=9.8(0.345) for 𝑛≥1
  • D𝑢=9.8(2.899) for 𝑛≥1
  • E𝑢=3.38𝑟 for 𝑛≥1

Q3:

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

  • A𝑎=5×(3)
  • B𝑎=5×(3)
  • C𝑎=3×(5)
  • D𝑎=3×(5)
  • E𝑎=3×(5)

Q4:

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

  • A−76×2
  • B−76×12
  • C−76×2
  • D−76×12

Q5:

Find, in terms of 𝑛, the general term of the sequence 1,19,181,1729.

  • A19()
  • B19−1
  • C19()
  • D19

Q6:

Find the first three terms of a geometric sequence given 𝑎=−3,616 and the common ratio is −2.

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

Q7:

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

  • A−2, 6, −18
  • B16, −118, 154
  • C−12, 16, −118
  • D6, −18, 54
  • E6, −2, 23

Q8:

Find the order of the term whose value is 4,374 in the geometric sequence 𝑎=23(3).

Q9:

Find the number of terms of the geometric sequence 112,56,28,…,74.

Q10:

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

This lesson includes 30 additional questions and 271 additional question variations for subscribers.

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