Question

What is a rule for the nth term of Geometric sequence -3,-6,-12,-24,-48

Answer 1

The sequence is given as,

`-3,\text{ -6, -12, -24, -48.......}`

For the given sequence,

`\begin{gathered} First\text{ term\lparen a\rparen = -3} \\ Common\text{ ratio\lparen r\rparen = }(-6)/(-3)=\text{ 2} \end{gathered}`

nth term of a geometric progression is given as,

`a_n\text{ = ar}^(n-1)`

Where,

a = First term

r = common ratio

Therefore the nth term is calculated as,

`a_n=\text{ -3\lparen2\rparen}^(n-1)`

Thus the required answer is,

`a_n=\text{ -3\lparen2\rparen}^(n-1)`