Question

Find the next term of the following sequence.

25, 10, 4, ...

Answer 1

https://answers.yahoo.com/question/index?qid=20100505133840AAyEeWa

Answer 2

formula to find next term of geometric sequence
\[\huge\rm r= \frac{ a_2 }{ a_1 } , \frac{ a_3 }{ a_2 } ,\frac{ a_4 }{ a_3 }\]
you should get same number
and for arithmetic sequence \[\huge\rm d =a_2 -a_1 \] \[a_3 - a_1 \]

Answer 3

it is geometric sequence \[a_1,a_1q,_1q^2,...\\q=\frac{a_2}{a_1}=\frac{a_3}{a_2}\\q=\frac{10}{25}=\frac{4}{10}\\q=\frac{2}{5}\\a_n=a_1q^{n-1}\\a_1=25\\a_2=10=25*\frac{2}{5}\\a_3=a_1q^2=10*\frac{2}{5}\\a_4=a_1q^3=4*\frac{2}{5}\]