Correct Answer - Option 2 : 512
Concepts:
Let us consider the sequence a1, a2, a3 …. an is a G.P.
- Common ratio = r = \(\frac{{{a_2}}}{{{a_1}}} = \frac{{{a_3}}}{{{a_2}}} = \ldots = \frac{{{a_n}}}{{{a_{n - 1}}}}\)
- nth term of the G.P. is an = arn−1
- Sum of n terms = s = \(\frac{{a\;\left( {{r^n} - 1} \right)}}{{r - 1}}\); where r >1
- Sum of n terms = s = \(\frac{{a\;\left( {1 - {r^n}} \right)}}{{1 - r}}\); where r <1
- Sum of infinite GP = \({{\rm{s}}_\infty } = {\rm{}}\frac{{\rm{a}}}{{1{\rm{}} - {\rm{r}}}}{\rm{}}\); |r| < 1
Where a is 1st term and r is common ratio.
Calculation:
Let 'a' be the first term and 'r' be the common ratio.
We know that Tn = a rn-1
Given: ar4 = 2
Now, Product of 9 terms = a × ar × ar2 × ar3 × ar4 × ar5 × ar6 × ar7 × ar8
= a
9 r
36 = (ar
4)
9 = 2
9 = 512