Question

consider the following (k-4) ; (k+1) ;m ; 5k ... the first 3 terms are arithmetic the last 3terms are geometric. .. determine the values of m and k if both are positive integers

Answer 1

clearly the common difference is 5, from the first two terms.

so, m-(k+1) = 5

now, the common ratio tells us that

m/(k+1) = 5k/m

solving both those equations, we get
(k,m) = (4,10)

and the terms are

0,5,10,20

and you can see the AP and GP

Answer 2

You can calculated my question where ,asking like that ,consider the following term (k-4),(k-1),m,5k