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If the product of three terms in a GP is 27 . Find its middle term.
1. 3
2. 9
3. 27
4. 6

1 Answer

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Best answer
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

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