Answer to Question #247365 in Algebra for M.l

Question

14 pairwise different positive integers are written on the board. Their mean value is equal to 19. Let M be the largest of these numbers. Find the smallest possible value of M.

Answer 1

given

mean value of these integers=19

total number of integers=14

mean value=sum of numbers$\div$ total number of integers

19=sum of numbers$\div$ 14

sum of numbers=$19\times 24$

As we sum in A.P

$s_n=\frac{n}{2}[2a+(n-1)d]\\n=14\\s_n=19\times 14\\d=1\space (unique \space difference)$

$19\times14=\frac{14}{2}[2a+(14-1)1]\\19=\frac{1}{2}[2a+13]\\38=2a+13\\2a=25\\a=12.5 \ is smallest possible value of M$