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.

Q1:

Find the value of the second term of the geometric sequence 𝑎=16×2, where 𝑛1.

  • A83
  • B13,888
  • C163
  • D323

Q2:

The recursive formula for a geometric sequence is 𝑎=0.345𝑎 and 𝑎=9.8 for 𝑛1. Give an explicit formula for the sequence.

  • A𝑎=9.8(0.345) for 𝑛>0
  • B𝑎=9.86.419(𝑛1) for 𝑛0
  • C𝑎=9.8(0.345) for 𝑛0
  • D𝑎=9.8(2.899) for 𝑛0
  • E𝑎=3.38𝑟 for 𝑛0

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,.

  • A76×2
  • B76×12
  • C76×2
  • D76×12

Q5:

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

  • A19()
  • B191
  • 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.

  • A2, 6, 18
  • B16, 118, 154
  • C12, 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,.

Practice Means Progress

Download the Nagwa Practice app to access 90 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.