mirender mirender

15-07-2016
Mathematics

Answered

find the sixth term of a geometric sequence with t5=24 and t8=3

Verified Answer :

15-07-2016

Hello,

\(t_{2}=t_{1}*q\\ t_{3}=t_{2}*q=t_{1}*q^{2}\\ ...\\ t_{5}=t_{1}*q^{4}\\ t_{8}=t_{1}*q^{7}\\\\ \dfrac{3}{24}= \dfrac{1}{8}=\dfrac{t_{8}}{t_{5}}= \dfrac{t_{1}*q^{7}}{t_{1}*q^{4}}=q^{3}\\ q= \frac{1}{2} \\ t_{6}=t_{5}*q=24* \dfrac{1}{2}=12\\\)

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