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Helen [10]
3 years ago
14

The 4th and 8th term of a G.P. are 24 and 8/27 respectively. find the 1st term and common ratio

Mathematics
1 answer:
beks73 [17]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric progression is

• a_{n} = a₁ r^{n-1}

where a₁ is the first term and r the common ratio

given a₄ = 24, then

a₁r^{3} = 24 → (1)

Given a₈ = \frac{8}{27}, then

a₁r^{7} = \frac{8}{27} → (2)

Divide (2) by (1)

r^{4} = \frac{\frac{8}{27} }{24} = \frac{1}{81}

Hence r = \sqrt[4]{\frac{1}{81} } = \frac{1}{3}

Substitute this value into (1)

a₁ × (\frac{1}{3} )³ = 24

a₁ × \frac{1}{27} = 24, hence

a₁ = 24 × 27 = 648

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Answer:

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Step-by-step explanation:

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3 years ago
Duncan takes a break from studying and goes to the gym to swim laps. If swimming burns 9.05×105 cal per hour, how many kilojoule
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For this case we have to by definition:

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1 kilocalorie equals 1000 calories

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The television station has received/A many complaints about/B
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Learn more about television station

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