If the integer 'k' is added to each of the numbers 36, 300, 596, one obtains the squares of the - Maths - Sequences and Series

Question

If the integer 'k' is added to each of the numbers 36, 300, 596,
one obtains the squares of the numbers of three consecutive terms
in an A P Find 'k'

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Terms In A
P area , a+d , a+2dSquares of the number of three consecutive terms in A
Pa2 , a+d2 , a+2d2a2 , a2+2ad+d2 , a2+4ad+4d2Now ,36+k , 300+k , 596+k are also the squares of the number of three consecutive terms in A
PSo,a2=36+k   
 1a2+2ad+d2=300+k   
2a2+4ad+4d2=596+k   
 3Subtracting 1 from 2 , we get2ad+d2=264   
 4Subtracting 2 from 3 , we get2ad+3d2=296   
 5Subtracting4 from 5 , we g2d2=32d2=16d=±4Substituting the value of d=4 in 4 , we get2a4+42=2648a+16=2648a=248a=31Substituting the value of d=-4 in 4 , we get2a-4+-42=264-8a+16=264-8a=248a=-31Now , substituting a=31 in 1, we get312=36+k961=36+k925=kValue of k is 925 
Now , substituting a=-31 in 1, we get-312=36+k961=36+k925=kValue of k is 925 
Thus k is equal to 925 
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If the integer 'k' is added to each of the numbers 36, 300, 596, one obtains the squares of the numbers of three consecutive terms in an A.P. .Find 'k'.