If the 2nd term of a G P is frac 8 9 and the 6t... - JAMB Mathematics 2016 Question
If the 2nd term of a G.P is \(\frac{8}{9}\) and the 6th term is 4\(\frac{1}{2}\). Find the common ratio.
A
2
B
\(\frac{3}{2}\)
C
\(\frac{2}{3}\)
D
3
correct option: b
T2 = \(\frac{8}{9}\), T6 = 4\(\frac{1}{2}\)
ar = \(\frac{8}{9}\)
ar5 = \(\frac{9}{2}\)
\(\frac{ar}{ar^5}\) = \(\frac{8}{9}\) x \(\frac{2}{9}\)
\(\frac{1}{r^4}\) = \(\frac{16}{81}\)
r = \(\sqrt[4]{18/16}\) = \(\frac{3}{2}\)
ar = \(\frac{8}{9}\)
ar5 = \(\frac{9}{2}\)
\(\frac{ar}{ar^5}\) = \(\frac{8}{9}\) x \(\frac{2}{9}\)
\(\frac{1}{r^4}\) = \(\frac{16}{81}\)
r = \(\sqrt[4]{18/16}\) = \(\frac{3}{2}\)
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