Question

If the 4th and 8th terms of a G.P are 256 and 16 respectively. Find the 3rd term

Answer 1

Answer:

Third Term = 512

Step-by-step explanation:

Let the first term be a

Common Ratio = r

$Fourth \ Term = ar^{3} = 256$

$Fifth \ Term = ar^{7} = 16$

$Dividing \ both \ equation :$

⇒ $\frac{ar^{7}}{ar^{3}} = r^{4} = \frac{16}{256} = \frac{1}{16}$

⇒ $r^{4} = \frac{1}{2^{4}} = (\frac{1}{2} )^{4}$

⇒$r = \frac{1}{2}$

∵ $ar^{3} = a (\frac{1}{2} )^{3} = \frac{a}{8} = 256$

a = 256 × 8 = 2048

$Third \ term = ar^{2} = 2048 (\frac{1}{2} )^{2} = \frac{2048}{4} = 512$