Question

If 5th term and 8th term of a gp be 48and384 respectively find the gp if terms of gp are real number

Answer 1

T5=48. T8=384
ar^4=48. ar^7=384
ar^7/ar^4=384/48
r^3=8
r=2. ar^3=48
a*8=48
a=6
The GP is 6, 12, 24, 48.........

Answer 2

The given GP becomes 3,5,12,24,...

• The 5th term of the GP is 48 and the 8th term of the GP is 384.

• nth term of the GP is given by the formula $t_n = ar^{n-1}$.

• Now,

$t_5 = ar^{5-1}$

$48= ar^{4}$    (Equation 1)

$t_8 = ar^{8-1}$

$384 = ar^{7}$        (Equation 2)

• Now dividing equation 2 by equation 1 , we get

8 = r³

r = 2

• Now substituting the value of d in equation 1 we get,

$ar^4 = 48$

$a3^4 = 48$

a = 3.

• Now the given series in GP becomes a , ar, ar² , ar³ ,...

• The given GP is 3 , 6 , 12 , 24 , .....