Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is -${1 \over 2}$ , then the greatest number amongst them is:

Let the A.P is <br>a - 2d, a - d, a, a + d, a + 2d <br>$\because$ sum = 25 <br>$\Rightarrow$ 5a = 25 $\Rightarrow$ a = 5 <br><br>Also given, <br><br> product (a² – 4d²) (a² – d²).a = 2520 <br><br>$\Rightarrow$ (25 – 4d²) (25 –d²)5 = 2520 <br><br>$\Rightarrow$ 4d⁴ – 121d² – 4d² + 121 = 0 <br><br>$\Rightarrow$ (d² – 1) (4d² – 121) = 0 <br><br>$\Rightarrow$ d = $\pm$1, d = $\pm {{11} \over 2}$ <br><br>When d = $\pm$1 we can't get any fraction term like -${1 \over 2}$. <br><br>$\therefore$ d = $\pm {{11} \over 2}$ <br><br>And when d = ${{11} \over 2}$ <br><br>we get largest term = 5 + 2d = 5 + 11 = 16