The 6th term of a geometric progression (GP) is 48. The first term is 1.5. What is the common ratio (CR)?
2.0
For a GP, the n-th term is \(a_n = a \cdot r^{\,n-1}\), where a is the first term and r is the common ratio.
Step 1 — Substitute the given values:
\(a_6 = 1.5 \cdot r^{\,5} = 48\)
Step 2 — Solve for \(r^{\,5}\):
\(r^{\,5} = \dfrac{48}{1.5} = 32\)
Step 3 — Take the fifth root:
\(r = 32^{1/5} = 2\)
Hence the common ratio is 2.0. The answer is option A.
Important Questions from Geometric Progression
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