Find the seventh term of the geometric sequence if a1 = 7 and r = 3

Answers

Answer 1

Answer:

The seventh term is 5,103.

Explanation:

Hey there!

We're given the initial term and the common ratio of an undetermined geometric sequence.

The formula to determine a geometric sequence is [tex]x_n = ar^{(n-1)}[/tex].

We know that a₁ is 7 and that r is 3. However, we don't know what n is. Our variable n is a stand in for the position in the sequence. Since we want 7 terms, we are going to have terms 1, 2, 3, 4, 5, 6, and 7. The variable n will equal each one of these.

Finally, our term xₙ is equivalent to the term we are trying to find, so it is a standalone variable.

Let's find all seven terms using the above formula.

We already have our first term: 7. Therefore, we set n equal to 2 and solve for xₙ.

Term 2

[tex]x_n = 7(3)^{(2-1)}\\x_n = 7(3)^1\\x_n = 7(3)\\x_n = 21[/tex]

Term 3

[tex]x_n = 7(3)^{(3-1)}\\x_n = 7(3)^2\\x_n = 7(9)\\x_n = 63[/tex]

Term 4

[tex]x_n = 7(3)^{(4-1)}\\x_n = 7(3)^3\\x_n = 7(27)\\x_n = 189[/tex]

Term 5

[tex]x_n = 7(3)^{(5-1)}\\x_n = 7(3)^4\\x_n = 7(81)\\x_n = 567[/tex]

Term 6

[tex]x_n = 7(3)^{(6-1)}\\x_n = 7(3)^5\\x_n = 7(243)\\x_n = 1701[/tex]

Term 7

[tex]x_n = 7(3)^{(7-1)}\\x_n = 7(3)^6\\x_n = 7(729)\\x_n = 5103[/tex]

We have found the seventh term to be 5,103.

The sequence is written as 7, 21, 63, 189, 567, 1,701, 5,103... (it will be ongoing if you wanted to calculate the next term).


Related Questions

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c. Bombay, India​

Answers

Answer:

Greenwich, England

Answer:

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Find the measure of the indicated angles.
M

Answers

Answer:

m<B = 83°

Explanation:

The figure given is a parallelogram having opposite sides that area parallel to each other. Therefore, opposite angels are congruent while the adjacent angles are supplementary.

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Answers

Answer:

evaporation/transpiration evaporation from the sea infiltration into the ground runoff into a river runoff into the sea

Explanation:

In hydrologic cycle, it shows the different pathways through which the water circulates in the environment leading to balanced biotic system. Just like air cycle, hydrologic cycle helps in keeping the living things like plants, humans in existence as well as aiding the non-living things like soil deposit, decayed plants materials, humus etc in equitable distribution.

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Answer:

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Answer the following in COMPLETE SENTENCES,
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Paragraph 1
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The tropical cyclones have a thermal origin, and they develop over tropical seas during late summers (August to mid-November). At these locations, the strong local convectional currents acquire a whirling motion because of the Coriolis force.

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Answer:

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#Carry on learning o(〃^▽^〃)o

Please answer it right (NO spam) I will give Brilliant

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Explanation:

The study is intended to understand the people's voting behavior in the upcoming presidential election of the USA. The population is the set of electoral votes is based on the congressional representation for each state. In general, primaries use secret ballots for voting. In 1936, the American Institute of Public Opinion also carried out a poll asking voters about their intentions in the upcoming presidential election.Roughly the same chance of being called as anyone else living in the United States who has a telephone.A new Pew Research Center analysis of survey questions from nearly a year’s worth of its public opinion polling finds that errors of the magnitude seen in some of the 2020 election polls would alter measures of opinion on issues by an average of less than 1 percentage point. By 49% to 40%, registered voters are more likely to say the Republican Party, rather than the Democratic Party, can do a better job on the economy.

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Answer:

Winds near the core of the cyclone can exceed 110 mph (50 meters/second). ... Tropical cyclones require warm surface waters at least 80°F (27°C). During the late summer months, sea surface temperatures reach their highest levels and provide tropical cyclones with the energy they need to develop into major storms.

Explanation:

;)

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Answer:

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Answer:

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Select one:

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Answer:

A population of snails and a population of sea urchins live in the same ecosystem. Both species rely on kelp as a food source. A population of snails and a population of sea urchins live in the same ecosystem. Both species rely on kelp as a food source. =The population of snails will likely decrease.

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