Question

The 3rd and the 8th term of a G. P. are 4 and 128 respectively. Find the G. P.

Answer 1

Answer:

$1, 2, 4, 8, .....$

Step-by-step explanation:

Let the first term of the GP be $a$ and common ratio be $r$

Then the GP will be

$a,ar,ar^2,ar^3,....$

Third term of GP

$a_3=ar^2$

or, $ar^2=4$   ..........(1)

Eighth term of GP

$a_8=ar^7$

or, $ar^7=128$   ..........(2)

Dividing eq (2) by eq (1)

$\frac{ar^7}{ar^2}=\frac{128}{4}$

$\implies r^5=32$

$\implies r^5=2^5$

$\implies r=2$

Putting the value of r in eq (1) we get

$a\times 2^2=4$

$\implies a\times 4=4$

$\implies a=1$

Therefore, the GP is

$1, 2, 4, 8, .....$

Hope this helps.