Lesson Worksheet: Finding the nth Term of a Geometric Sequence Mathematics
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 how to find a term’s order given its value.
Q5:
Find the first three terms of the geometric sequence given their sum is and the sum of their squares is 21.
- A,,
- B,,
- C,,
- D,,
Q8:
The numbers 38 and 4,864 are terms of a geometric sequence. The ratio of the sum of the two terms after 38 in the sequence to the sum of the two terms before 4,864 in the sequence is . How many terms lie between 38 and 4,864 in the sequence?
Q12:
Find the value of given the of the geometric sequence is three times greater than the of the geometric sequence .
Q13:
The sum of the first and second terms of a geometric sequence is 54 and . Find the possible values of .
- A or
- B144 or 432
- C72 or
- D9 or 27
Q14:
Find, in terms of , the general term of the sequence .
- A
- B
- C
- D
Q16:
Find the order and value of the first term whose value is less than 0.0049 in the geometric sequence .
- A,
- B,
- C,
- D,
- E,
Q17:
Suppose that and belong to a geometric sequence with a positive . Using four decimal places for your common ratio, determine this first term to two decimal places.
- A
- B
- C
- D
- E
Q18:
Find the number of terms of the geometric sequence .
Q19:
In the following geometric sequence, find the lowest term order, , so that the value of the term is less than one,.
Q20:
Find the second term of a geometric sequence given , and all terms are positive.
Q21:
Find the geometric sequence given the first term is 3 and the fourth term is 81. Then find the order of the term whose value is 729.
- A, 6
- B, 5
- C, 5
- D, 6
- E, 6
Q22:
What is the order of the term in the geometric sequence whose value is 1,572,864?
Q24:
Determine and that make a geometric sequence, starting at , of the form .
- A,
- B,
- C,
- D,
- E,
Q25:
Find the order of the first term whose value is greater than 500 in the geometric sequence .
- A,
- B,
- C,
- D,
- E,