# Worksheet: Finding the nth Term of a Geometric Sequence

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 , ,

**Q6: **

Find the order of the term in the geometric sequence .

**Q7: **

Find the second and third terms of a geometric sequence given , and all terms are positive.

- A ,
- B ,
- C ,
- D ,
- E ,

**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?

**Q9: **

In a geometric sequence and for a certain , we have , , and . Find the first 3 terms of the sequence and what is.

- A , and
- B , and
- C , and
- D , and
- E , and

**Q10: **

Find, in terms of , the general term of the sequence where .

- A
- B
- C
- D

**Q11: **

Determine and that make the following a geometric sequence, starting at , of the form :

- A ,
- B ,
- C ,
- D ,
- E ,

**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

**Q15: **

Find the order of the term whose value is 4,374 in the geometric sequence .

**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: **

Find the order of the first term whose value is less than one in the geometric sequence .

**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?

**Q23: **

Find, in terms of , the general term of the sequence .

- A
- B
- C
- D

**Q24: **

Find the geometric sequence given and the common ratio is 4.

- A
- B
- C
- D
- E

**Q25: **

Determine and that make a geometric sequence, starting at , of the form .

- A ,
- B ,
- C ,
- D ,
- E ,