Sequences & Series  Geometric  the General term.
Test Yourself 1.
Finding a term  1.
T_{n} = 3×2^{n}.
T_{5} = 3 × 2^{5} = 96. 
2. T_{1} = 2 and r = 5
T_{6} = 2 × 5^{5} = 6,250 
3. T_{1} = 5 and r = 4
T_{8} = 5 × (4)^{7}= 81,920 
4. T_{1} = 3 and T_{4} = 192
∴ 192 = 3× r^{3} r^{3} = 64 r = 4 First four terms are 3, 12, 48 and 192. 

Finding a 1^{st} term  5. T_{3} = 18 and r = 3
18 = T_{1} × 3^{2} T_{1} = 2 
6. 
Finding a difference  7.  8. 
Finding the number of terms  9.  10. 
Given 2 terms  11.  12. 
13.  14.  
Miscellaneous  15.  16. 
17. The three terms are in geometric progression and so they have the same ratio between them. The ratio can be calculated in 2 different ways  by ratioing the 2^{nd} term to the 1^{st} term and then the 3^{rd} term to the 2^{nd} term. As these are the same, equate them.  18. Same approach as for the previous question. Calculate the common ratio in two different ways and equate the results.  
19.  20. 