Question

8. Find the geometric series whose 5th and 8th terms are 80 and 640 respectively. 1 -1 noctivol​

Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\geometric \: series \: \: GP \\ \\ so \: we \: know \: that \\ for \: GP \: \\ tn = a.r {}^{n - 1} \\ t5 = a.r {}^{5 - 1} \\ 80= a.r {}^{4} \: \: \: \: \: \: (1) \\ \\ similarly \\ t8 = a.r {}^{8 - 1} \\ 640 = ar {}^{7} \: \: \: \: \: \: (2)$

$applying \: now \: \frac{(1)}{(2)} \\ we \: get \\ \\ \frac{80}{640} = \frac{a.r {}^{4} }{a.r {}^{7} } \\ \\ \frac{1}{8} = \frac{1}{r {}^{3} } \\ \\ applying \: invertendo\\ we \: have \\ \\ r {}^{3} = 8 \\ r = 2$

$substitute \: value \: of \: r \: in \: (1) \\ we \: get \\ \\ 80 = a.r {}^{4} \\ = a.(2) {}^{4} \\ 16a = 8 0 \\ a = 5$

$so \: thus \: then \\ terms \: in \: GP \: are \: given \: by \\ a = 5 \\ ar = 5 \times 2 = 10 \\ ar {}^{2} = 5 \times (2) {}^{2} = 5 \times 4 = 20 \\ \\ thus \: the \: required \: GP \: is \\ 5 \: ,10 \: ,20 \: , \: and \: so \: on$

Answer 2

Answer:

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