What are first terms of this sequence: f(1)=-2, f(n)=f(n-1)+4?

1 Answer
Jan 8, 2017

Answer:

#n=1->a_1=-2 larr" given value"#

#n=2->a_2=-2+4 = 2#
#n=3->a_3=-2+4+4 = 6#
#n=4->a_4=-2+4+4+4=10#

Explanation:

Let the place count be #n#
Let the #n^("th")# term be #a_n#

Given #f(n=1)=-2 #

We are also told that any one term is the previous term + 4.
This is derived from #f(n)=f(n-1)+4# where #f(n-1)# is the previous term.

Consequently we have an Arithmetic sequence with common difference of +4

From this the sequence is:

#n=1->a_1=-2 larr" given value"#

#n=2->a_2=-2+4 = 2#
#n=3->a_3=-2+4+4 = 6#
#n=4->a_4=-2+4+4+4=10#

And so on. Also from this we also have an alternative equation for any #a_n# in that we have:

#a_n =-2+4(n-1)#