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.
Find the first three terms of the geometric sequence given their sum is and the sum of their squares is 21.
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?
Find the value of given the of the geometric sequence is three times greater than the of the geometric sequence .
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
Find, in terms of , the general term of the sequence .
Find the order and value of the first term whose value is less than 0.0049 in the geometric sequence .
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.
Find the number of terms of the geometric sequence .
In the following geometric sequence, find the lowest term order, , so that the value of the term is less than one,.
Find the second term of a geometric sequence given , and all terms are positive.
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
What is the order of the term in the geometric sequence whose value is 1,572,864?
Determine and that make a geometric sequence, starting at , of the form .
Find the order of the first term whose value is greater than 500 in the geometric sequence .