A) 21, 17, 13
B) 20,16, 12
C) 22, 18, 14
D) 24, 20, 16
Correct Answer: A
Solution :
Let consecutive terms of an A.P. are \[a-d,\ a,\ a+d\]. Under given condition, \[(a-d)+a+(a+d)=51\] \[\Rightarrow \] \[a=17\] and \[(a-d)(a+d)=273\]\[\Rightarrow \]\[{{a}^{2}}-{{d}^{2}}=273\] \[\Rightarrow \] \[-{{d}^{2}}=273-289\]\[\Rightarrow \]\[d=4\] Hence consecutive terms are 13, 17, 21. Trick: Both conditions are satisfied by (a) \[i.e.\] 21, 17, 13.
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