Question

-1,-7,-49 nth term please help me please

Answer 1

a(n) =
`- \frac{ {7}^(n) }{7}`

Answer 2

`a_n=(-1) \cdot 7^(n-1)`

Explanation:

`\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^(n-1)$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}`

Given sequence:

• -1, -7, -49, ...

The given sequence is a geometric sequence since there is a common ratio between consecutive terms.

To calculate the common ratio, divide consecutive terms:

`\implies r=(a_2)/(a_1)=(-7)/(-1)=7`

`\implies r=(a_3)/(a_2)=(-49)/(-7)=7`

Therefore, the common ratio, r, is 7.

Substitute the found value of r and the first term, -1, into the formula to create an equation for the nth term:

`\implies a_n=(-1) \cdot 7^(n-1)`