Question

7. Here is a sequence.

2, 2√7, 14, 14√7

Find the nth term


This is geometric sequences​

Answer 1

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?

Answer 2

`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)`