Question

Sum of three terms of a GP is 57,product of the terms is 343 find GP

Answer 1

LET THE 3 TERMS OF GP BEa/r ,a ,ar
So their products is =a/r×a×ar=343
So r cancels...
a3=343
a=7... (7×7×7=343)
Their sum is a/r , a,ar=57
Place the value of a
7/r 7,7r
Take LCM..SO IT WILL BE
7+7r+7r^=57r (division when comes to othr side it becomes multiplication)
7+7r^=57r-7r
7+7r^=50r
Std form is 7r^-50r+7
7×7=49..
49×1=49 and 49+1=50
7r^-49r-1r+7
7r (r-7)-1 (r-7)
7r-1 or r-7
So r =7..
So gp is 7,49,343....