Question

The $5^{th}and{8}^{th}$ terms of a G.P. are 48 and 384 respectively. Find the G.P. if terms of G.P. are real numbers.

• A.
  $0,2,10,14,...$
• B.
  $3,6,12,24,...$
• C.
  $8,20,35,40,...$
• D.
  $5,10,15,20,...$

Answer 1

The correct option is B

$3,6,12,24,...$
Let first term be a and common ratio be 'r'

$a_5=a{r}^4,a_8=a.r^7\frac{a_8}{a_5}=\frac{384}{48}\Rightarrow \frac{a.r^7}{a.r^4}=\frac{384}{48}\Rightarrow r=\sqrt[3]{38}=2a_5=48\Rightarrow a.r^4=48\Rightarrow a.(2{)}^4=48\Rightarrow 16a=48\therefore a=3a_1=a=3a_2=ar=3\times 2=6a_3=a{r}^2=3\times 2^2=12a_4=a{r}^3=3\times 2^3=24TherequiredGPis3,6,12,\mathrm{24...}$
Hence, option b is correct.