Question

Five numbers are in ap .sum is 25 .product is 2520 and one number is -1/2 .then greatest number

Answer 1

Answer:

Greatest number among them is $16$.

Step-by-step explanation:

Given :-

• Five numbers are in arithmetic progression.
• Product is 2520.
• One of the number is $\frac{-1}{2}$.

To find :-

• The greatest number among them is ?

Solution :-

Let the A.P is :-

$(a-2d),(a-d),(a),(a+d),(a+2d)$

Given that :-

Sum = 25 so a = 5

Product is 2520

So :-

$(25-4d^2)(25-d^2)\;=\;504$

$4d^4-125d^2+121\;=\;0$

$d^2\;=\;1,\frac{121}{4}\;\rightarrow\;$ ±$1$ $,$ ±$\frac{11}{2}$

$d\;=\;$ ±$1$ is rejected because none of the term can be $\frac{-1}{2}\;$ $\;\;\rightarrow\;d\;=\;\frac{11}{2}$

∴ The A.P will be $-6,\frac{-1}{2},5,\frac{21}{2},16$ and the greatest number among them is $16$.