If the last term of a geometric progression is 1 and the common ratio (r) is \(\displaystyle\frac{1}{2}\), then the total number of terms in this geometric progression is _____ if the first term is 16.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
In a geometric progression the \(n\)th term is \(ar^{n-1}\). Setting it equal to the last term gives the number of terms.
\(16\times\left(\displaystyle\frac{1}{2}\right)^{n-1}=1\)
\(\left(\displaystyle\frac{1}{2}\right)^{n-1}=\frac{1}{16}=\left(\frac{1}{2}\right)^{4}\)
\(n-1=4\), so \(n=5\)