In a geometric progression, if the product of the first three terms is \(\frac{27}{8}\), then its second term is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{3}{2}\)
In a geometric progression each term is the one before it multiplied by the common ratio \(r\). Writing the first three terms around the middle term \(a\) makes \(r\) cancel in the product.
The three terms: \(\displaystyle \frac{a}{r},\ a,\ ar\)
Their product: \(\displaystyle \frac{a}{r}\times a\times ar=a^3=\frac{27}{8}\)
Second term: \(\displaystyle a=\sqrt[3]{\frac{27}{8}}=\frac{3}{2}\)