Find the first term of a GP if the third term i... - SS2 Mathematics Sequence and Series Question
Find the first term of a GP if the third term is \(72\) and the sixth term is \(243\).
A
\(21\frac{1}{3}\)
B
\(19\frac{2}{3}\)
C
\(31\frac{1}{3}\)
D
21
correct option: a
Assume the 3rd term is the geometric mean of the 1st and 6th terms
\[Geometric\ mean,\ GM\ = \ \sqrt{al}\]
\[72 = \sqrt{a \times 243}\]
\[72^{2} = 243a\]
\(a = \frac{72^{2}}{243} = 21.3\)
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