How do you find the nth term rule for #2,10,50,250,...#?

1 Answer
Aug 3, 2016

Answer:

#n^(th)# term = #t_n=2*5^(n-1)#, where, #n in NN#.

Explanation:

Let us note that, in the given seq., every succeeding term is obtained by multiplying by #5# the preceding term.

In other words, this means that the given seq. is a Geometric Seq. with Common Ratio #r=5#.

The seq. has the First Term #a=2#.

The Formula for the General Term, or, #n^(th)# term, denoted as #t_n# is given by, #t_n=a*r^(n-1)#.

In our case, #t_n=2*5^(n-1)#, where, #n in NN#.