In Geometric Progression, if 10th term is 3072 and 6th term is 192. Then 3rd term will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
In a geometric progression the \(n\)th term is \(a r^{n-1}\). Dividing one given term by the other cancels \(a\) and leaves a power of the common ratio \(r\).
\(a r^{9}=3072\) (1)
\(a r^{5}=192\) (2)
Dividing (1) by (2), \(a\) cancels: \(\displaystyle r^{4}=\frac{3072}{192}=16\), so \(r=2\)
From (2): \(32a=192\), so \(a=6\)
Third term: \(a r^{2}=6\times4=24\)
(\(r=-2\) also gives \(r^{4}=16\), but then \(a=-6\) and the third term is \(-24\), which is not among the options.)