Mohamed and Li Jing were asked to find an explicit formula for the sequence -5\,,-25\,,-125\,,-625,...−5,−25,−1 25,−625,...Minus, 5, comma, minus, 25, comma, minus, 125, comma, minus, 625, comma, point, point, point.

the equation is given as

Explanation:

As the sequence is given as −5,−25,−125,−625,...

From this the first term is given as

a1=-5

Now the relation between this term and the next term is to be observed.

d=a2-a1=-25-(-5)=-25+5=-20

d=a3-a2=-125-(-25)=-125+25=-100

Now it is observed that the difference is not same this indicates that the relation is not arithmetic.

next up is the geometric sequence so the value of ratio is given as

r=a2/a1=-25/-5=5

r=a3/a2=-125/-25=5

As  the ratio is same this indicates, this is a geometric sequence.

Now for the geometric sequence, the value of the general term is given as

Here a1=-5 and r=5 so the equation is given as