How do you write the next 4 terms in each pattern and write the pattern rule given 7, 25, 79, 241, 727?
1 Answer
The next
A recursive rule is:
#{ (a_1 = 7), (a_(n+1) = 3a_n + 4) :}#
The general formula can be written:
#a_n = 3^(n+1)-2#
Explanation:
A recursive formula for the given sequence is:
#{ (a_1 = 7), (a_(n+1) = 3a_n + 4) :}#
That is: The first term is
Consider the sequence of powers of
#1, 3, 9, 27, 81, 243, 729,...#
Notice that if we discard the first two terms and subtract
So we can write a formula for a general term of the sequence as:
#a_n = 3^(n+1)-2#
Using the recursive formula, we find:
#a_6 = 3a_5+4 = 3*727+4 = 2185#
#a_7 = 3a_6+4 = 3*2185+4 = 6559#
#a_8 = 3a_7+4 = 3*6559+4 = 19681#
#a_9 = 3a_8+4 = 3*19681+4 = 59047#