Q66 / 180 · KCET 2015 · Mathematics

If the \( 2^{\text {nd }} \) and \( 5^{\text {th }} \) terms of G.P. are \( 24 \) and \( 3 \) respectively, then the sum of \( 1^{\text {st }} \) six terms
is

  • Correct answer
    A
    \( \frac{189}{2} \)
  • B
    \( \frac{189}{5} \)
  • C
    \( \frac{179}{2} \)
  • D
    \( \frac{2}{189} \)

Solution

Given that, $T_{2}=24$ and $T_{5}=3$ Now, $a r=24 \rightarrow(1)$ and $a r^{4}=3 \rightarrow(2)$ Dividing Eq. (2) by Eq. (1), we have $\frac{a r^{4}}{a r}=\frac{3}{24} \Rightarrow r^{3}=\frac{1}{8} \Rightarrow r=\frac{1}{2}$ So, from Eq. (1), we have $a=24 \times 2=48$ Therefore, $S_{6}=\frac{a\left(1-r^{5}\right)}{1-r}=\frac{48\left(1-(1 / 2)^{6}\right)}{1-1 / 2}=\frac{189}{2}$

Hence, the correct answer is option: 'A'.

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