Progressions. 113 



10. Prove that if quantities be in geometric progression their 

 differences are also in geometrical progression, having the same 

 common ratio as before. 



11. The first and sixth terms of a geometric progression are 

 I and 243 ; find the sum of six terms, commencing at the third. 



12. The first term of a geometric progression is 5 and the 

 ratio 2. How many terms of this series must be taken that their 

 sum may be equal to 33 times the sum of half as many terms ? 



A— 14 



