406 PRACTICAL MATHEMATICS 



Also u n = (1 + A) "MQ 



n(n 1) . n(n l)(n 2) 

 -n^ ' A 2 w + -i - j- - 1 



l_ L 



o i 



1 + 3n + - n(n -1) + - n(n - l)(w - 2) 

 2 t> 



{6 



9n 2 - 



= - {w 3 + 6w 2 + 



+ 6} 



This result enables us to find the value of any term by giving 

 n its necessary value. 



The 9th term is obtained by putting n = 8 



990 





and 



Mg = _ = 165 



Example 2. Find the 10th term and the general term of the 

 series 



M 5 = 121 



Working along the .diagonal line running downwards from 



M - 1, AM O = 4, A 2 M = 6 A 3 M = 4, and AX = 

 The 10th term is evidently M 9 , 

 and M 9 = (1 + A)X 



= MO + 9AM + 36A 2 M + 84A 3 M 

 = 1 + 9x4+36x6+84x4 

 = 589 

 also u n = (1 + A) "M O 



n(n 1) A n(n l}(n 2) . 



} A 2,. v jj n ; A 3 Mo 



- 2) 



