How many terms are there in the G.P.
3, 6, 12, 24....... 384?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8
In a G.P. each term is the one before it multiplied by the common ratio, so the \(n\)th term is \(a r^{\,n-1}\). The number of terms is the value of \(n\) for which this formula gives the last term, 384.
First term \(a=3\) and common ratio \(r=6\div3=2\)
Setting the \(n\)th term equal to the last term: \(3\times2^{\,n-1}=384\)
\(2^{\,n-1}=128\), which is \(2^7\)
Comparing the powers of 2: \(n-1=7\), so there are \(n=8\) terms