Sequences & Series  Geometric  the General term.
Test Yourself 2.
Finding a term  1. Show (without writing out all the terms of the series) that the 12^{th} term of the geometric series 64 + 32 + 16 is 1/32.  2. If 2p + 1, 5p and 12p  4 are the first three terms in a geometric sequence, find the value of p and hence find the n^{th} term. 
3. Which expression is a term in the geometric series 3x  6x^{2} + 12x^{3} ...?

4. Find the 9th term in the series:
1000, 100, 10, 1... Express your answer as a decimal. 

Finding a 1^{st} term  5.  6. 
Finding a ratio.  7.  8. 
Finding the number of terms  9. For the geometric series beginning
18 + 9 + 4.5 which term is that with a value just greater than 0.001? 
10. 
Given 2 terms  11. The third term of a geometric series is 36 and the sixth term is 972.
Find the common ratio and the first term of the series. 
12. 
Miscellaneous  15. The terms 2 + x + 3 form a geometric series. Find the possible values of x. 

17. The numbers 2  x, x and 5  x form a geometric sequence.
What is the value of x? 
18. 

19.  20. 