# 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