Correct Answer - Option 1 : 3
Concept:
If a, ar, ar2, ar3,.....,arn-1 are in GP then nth term of GP is given by Tn = arn-1
If a1, a2, a3, a4 are in GP, then the common ratio of GP is given by, \(\rm r=\frac{a_{2}}{a_{1}}=\frac{a_{3}}{a_{2}}=\frac{a_{4}}{a_{3}}\)
Note:
If we have to choose terms in GP where the product is given then we choose terms like \(\rm \frac{a}{r^{2}}, \frac a r, a ,ar, ar^2\)
If we have to choose terms in GP where the product is given then we choose terms like \(\rm \frac a r, a ,ar\)
Where a and r be the first term and common ratio of the GP.
Calculation:
Let us consider the three terms are \(\rm \frac a r, a ,ar\) respectively where a and r are the first term and common ratio of the GP.
Now, we have given
\(\rm \frac a r \times a \times ar\) = 27
a3 = 27
So, a = 3
So the middle term of the GP = a = 3