28 BOOK OF MATHEMATICAL PROBLEMS. 



144. Having given that 7 , - , , are in A. P. ; prove 



that 



a 8 + c a W _ a t- o + c 

 a' + c _ 2b* ~ 2 " 



145. If a, b, c; 5, c, a; or c, a, b be in A. P., then will 



9 

 and if in G. P., 



146. If a, I be the first and n ih terms of an A. p. the con- 

 tinued product of all the n terms is 



147. The first term of a G.P. is a, and the w th term l\ prove 

 that the r th term is (a n ~ r Z 1 " 1 )"^ 1 . 



148. If a, b, c be in A. P., a, ft y in H.P., and aa, 6ft cy in 

 .G. P., then will 



1 1 1 



a : o : c :: - : 75 : -. 

 y /3 a 



149. The first term of an H. p. is a and the n ih term I, prove 

 that the r" 1 term is 



Prove that the sum of these n terms < (a + 1) > a 11 ^ ^ e i r con ' 



n 



tinued product <(oZ) 8 . 



