Question

If x,2x+2,3x+3 are in (g.p).find the common ratio and the 4th term.

Answer 1

the common ratio must be term(3)/term(2)
= (3x+3)/(2x+2)
= 3(x+1) / (2(x+1) )
= 3/2

then term(4) = (3/2)(3x+3) = 9x/2 + 9/2

for extra marks, What is the value of x ?

(2x+2)/x = 3/2
4x + 4 = 3x
x = -4

Answer 2

Step by step explanation: let find ratio; r=d2/d1=d3/d2.then equal to, 2x+2/x =3x+3/2x+2,then cross multiply. (2x+2)^2=x(3x+3). 4x^2+8x+4=3x^2+3x. There4, x^2+5x+4=0 by solve the equation,we get x=-1or-4. So,when x=-1,the series is -1,0,0. So,t4=0. But when x=-4,the series is -4,-6,-9. So,1st term=-4 and r=3/2 and tn=ar^n-1. T4=-4*(3/2)^4-1, t4=-4*(3/2)^3. T4=-13.5 or -27/2.