The recursive sequence is defined by the formula #t_n=2t_(n-1)+3#; and #t_1=-2#, how do you find #t_6#?
2 Answers
Find
Explanation:
Note that as
So we can look for a general formula for terms of the form:
#t_n = 2^na + b#
for some constants
Then we find:
#2^na + b = t_n = 2t_(n-1)+3 = 2(2^(n-1)a + b) = 2^na+2b+3#
Hence we find
Then:
#-2 = t_1 = 2^1 a - 3 =2a-3#
Hence we find
So the general formula of a term of our sequence is:
#t_n = 2^(n-1)-3#
If you like, we can double check this formula:
#2t_(n-1)+3 = 2(2^(n-2)-3)+3 = 2^(n-1)-6+3 = 2^(n-1)-3 = t_n#
In particular:
#t_6 = 2^5-3 = 32-3 = 29#
Explanation:
Proposing
Making