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  • Fill in the blanks The sum of terms equidistant from the beginning and end in an A.P. is equal to ............ .

Fill in the blanks  The sum of terms equidistant from the beginning and end in an A.P. is equal to ............ .

Answers (1)

Taking first and last terms of

a_{1}+a_{n}=a+a+ \left( n-1 \right) d=2a+ \left( n-1 \right) d

Taking k-th and (n-k+1) -th term   

\\ a_{k}+a_{n-k+1}=a+ \left( k-1 \right) d+ \left( a+ \left( n-k+1-1 \right) d \right) \\\\ =2a+ \left( k-1+n-k+1-1 \right) d \\\\ =2a+ \left( n-1 \right) d \\\\ =a_{1}+a_{n} \\\\

 

 

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infoexpert21

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