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Question

If the seventh term of an A.P. is 19 and its ninth term is 17, find its (63)rd term. 


Solution

Nth term = a+ ( n-1 ) d
( where a is the first term, n is the no. of terms
and d is the difference between two consecutive terms . )

seventh term = a7 =    19
ninth term = a9 =   17
a7 = a + 6d - ( Eq 1 )
a9= a+ 8d - ( Eq 2 )
by subtracting ( 1 ) from ( 2 ) 
(+ )a+ 8d =  17 
( - )a+ 6d =    ( - )19 ( remember here the sign of 6d becomes -6d because of minus procedure)
 2d =   263          
 or d =   163          
by putting value of d in Eq. ( 2 )
a + 8  163          = 1/7
a +  863           = 1/7
a =   17           -  863          
a =  163          

   
a63  = a + 62d
= 163   + 62 163  
= 163   + 6263  
= 1 ans. 


Mathematics
RD Sharma
Standard X

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