A) 55
B) 45
C) 65
D) 75
Correct Answer: C
Solution :
Let the numbers in A.P. be a \[-\] 3d. a \[-\] d, a + d and a + 3d. \[\therefore \]a\[-\]d+ a+ d= 110 \[\Rightarrow \] 2a= 110 \[\therefore \] a = 55 Again, \[\left( a-3d \right)\left( a+3d \right)=2125\] \[\Rightarrow \]\[(55-3d)(55+3d)=2125\] \[\Rightarrow \]\[3025-9{{d}^{2}}=2125\] \[\Rightarrow \]\[3025-2125=9{{d}^{2}}\] \[\Rightarrow \]\[9{{d}^{2}}=900\] \[\Rightarrow \]\[{{d}^{2}}=100\Rightarrow d=10\] \[\therefore \]Third term =a+d \[=55+10=65\]
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