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3 votes
7. Here is a sequence.

2, 2√7, 14, 14√7

Find the nth term


This is geometric sequences​

User JohnDizzle
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2 Answers

4 votes

Answer: infinity if n is not specified.

Explanation:

What number is n?

If n is not specified, the nth term will be infinity because the geometric sequence will skyrocket?

User Ori Wasserman
by
8.2k points
2 votes

Answer:


a_n=2 \cdot \left(√(7)\right)^(n-1)

Explanation:

A geometric sequence is a sequence of numbers in which each term is determined by multiplying the preceding term by a constant factor known as the common ratio (r).

The general formula for the nth term of a geometric sequence is:


\boxed{\begin{array}{l}\underline{\sf Geometric \;sequence}\\\\a_n=ar^(n-1)\\\\\textsf{where:}\\\phantom{ww}\bullet \;\textsf{$a$ is the first term.}\\\phantom{ww}\bullet\;\textsf{$r$ is the common ratio.}\\\phantom{ww}\bullet\;\textsf{$a_n$ is the $n$th term.}\\\phantom{ww}\bullet\;\textsf{$n$ is the position of the term.}\\\\\end{array}}

Given geometric sequence:

  • 2, 2√7, 14, 14√7

Therefore, the first term (a) is 2, so:


a = 2

To find the common ratio (r), divide one term by its preceding term:


r=(a_2)/(a_1)=(2√(7))/(2)=√(7)

Substitute the values of a and r into the formula to create an equation for the nth term of the given sequence:


a_n=2 \cdot \left(√(7)\right)^(n-1)

User Miriam Suzanne
by
8.0k points

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