Question

Mohamed and Li Jing were asked to find an explicit formula for the sequence -5\,,-25\,,-125\,,-625,...−5,−25,−125,−625,...Minus, 5, comma, minus, 25, comma, minus, 125, comma, minus, 625, comma, point, point, point. Mohamed said the formula is g(n)=-5\cdot5^{\large{n}}g(n)=−5⋅5 n g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, end superscript, and Li Jing said the formula is g(n)=-5\cdot5^{\large{n-1}}g(n)=−5⋅5 n−1 g, left parenthesis, n, right parenthesis, equals, minus, 5, dot, 5, start superscript, n, minus, 1, end superscript. Which one of them is right? Choose 1 answer: Choose 1 answer:

Answer 1

Only Li Jing

Explanation:

This is because the formula −5 * 5 is worng as the first term is reapeated again so it is Li Jing

Answer 2

Li Jing

Explanation:

Given the sequence:

-5,-25,-125,-625,...

Mohamed's Formula is given as:
`g(n)=-5\cdot5^{\large{n}}`

Using Mohamed's formula:

`When\: n=1,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^(1)=-25\\When\: n=2,g(n)=-5\cdot5^{\large{n}}=-5\cdot5^(2)=-125\\`

Li Jing's Formula is given as:
`g(n)=-5\cdot5^{\large{n-1}}`

Using Mohamed's formula:

`When\: n=1,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^(1-1)=-5\\When\: n=2,g(n)=-5\cdot5^{\large{n-1}}=-5\cdot5^{\large{2-1}}=-25\\`

We can see that Li Jing's Formula produces the gien sequence.

Li Jing is Right.