A) \[\frac{21}{2}\]
B) 7
C) 27
D) 16
Correct Answer: D
Solution :
| [d] |
| Let 5 terms of A.P. be, \[a-2d,\text{ }a-d,\text{ }a,\text{ }a+d\] and\[a+2d\] |
| \[5a=25~\Rightarrow a=5\] |
| Also \[({{a}^{2}}-4{{d}^{2}})({{a}^{2}}-{{d}^{2}})a=2520\] |
| \[\Rightarrow 4{{d}^{4}}-125{{d}^{2}}+121=0\] |
| \[\Rightarrow ({{d}^{2}}-1)(4{{d}^{2}}-121)=0\] |
| \[d=\pm 1\] or \[d=\pm \,\frac{11}{2}\] |
| \[d=\pm \,1\] does not give any term as \[\frac{-1}{2}\] |
| Hence rejected |
| \[\therefore d=\frac{11}{2}\] |
| Greatest term \[=5+2\left( \frac{11}{2} \right)=16\] |
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