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The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively....

Further Mathematics
WAEC 2019

The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively. Find the sixth term of the sequence 

  • A. \(\frac{81}{32}\)
  • B. \(\frac{9}{8}\)
  • C. \(\frac{1}{4}\)
  • D. \(\frac{32}{729}\)
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Correct Answer: Option D
Explanation

ar = \(\frac{2}{9}\) .....(i) 

ar\(^3\) = \(\frac{8}{81}\) ......(ii) 

\(\frac{ar3}{ar} = \frac{8}{81} \times \frac{9}{2}\) 

r\(^2 = \frac{4}{9}\) 

r = \(\sqrt{\frac{4}{9}}\) 

= \(\frac{2}{3}\) 

ar = \(\frac{2}{9}\) 

a(\(\frac{2}{3}\)) = \(\frac{2}{9}\)

a = (\(\frac{2}{3}\)) = \(\frac{2}{9}\)

a = \(\frac{2}{9} \times \frac{3}{2}\)

a = \(\frac{1}{3}\) 

T\(_r\) = ar\(^5\) = (\(\frac{1}{3}\))(\(\frac{2}{5}\))\(^5\) 

= \(\frac{32}{729}\) 


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NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Join your school's WhatsApp group
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
Join your school's WhatsApp group
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts