5th term for recursive sequence:
a(1) = 1
a(n+1)=3a(n)-1
a(1) = 1
a( n + 1 ) = 3 a ( n ) - 1 = 0
a ( n + 1 ) = 3 a ( n ) - 1
a ( 0 + 1 ) = 3 a ( 0 ) - 1
a ( 1 ) = 3 a ( 0 ) - 1
1 = 3 a ( 0 ) - 1
Add 1 to both sides
1 + 1 = 3 a ( 0 ) - 1 + 1
2 = 3 a ( 0 )
Divide both sides by 3
2 / 3 = a ( 0 )
a ( 0 ) = 2 / 3
n = 1
a ( n + 1 ) = 3 a ( n ) - 1
a ( 1 + 1 ) = 3 a ( 1 ) - 1
a ( 2 ) = 3 ∙ 1 - 1
a ( 2 ) = 3 - 1
a ( 2 ) = 2
n = 2
a ( n + 1 ) = 3 a ( n ) - 1
a ( 2 + 1 ) = 3 a ( 2 ) - 1
a ( 3 ) = 3 ∙ 2 - 1
a ( 3 ) = 6 - 1
a ( 3 ) = 5
n = 3
a ( n + 1 ) = 3 a ( n ) - 1
a ( 3 + 1 ) = 3 a ( 3 ) - 1
a ( 4 ) = 3 ∙ 5 - 1
a ( 4 ) = 15 - 1
a ( 4 ) = 14
n = 4
a ( n + 1 ) = 3 a ( n ) - 1
a ( 4 + 1 ) = 3 a ( 4 ) - 1
a ( 5 ) = 3 ∙ 14 - 1
a ( 5 ) = 42 - 1
a ( 5 ) = 41
a(1) = 1
a(2) = 3a(1)-1 = 3-1 = 2
a(3) = 3a(2)-1 = 6-1 = 5
a(4) = 3a(3)-1 = 15-1 = 14
a(5) = 3a(4)-1 = 42-1 = 41
To find the 5th term of the recursive sequence, we need to use the given rule:
a(1) = 1
a(n+1) = 3a(n) - 1
Step 1: Find the values for the first few terms by following the recursive rule.
a(1) = 1
a(2) = 3a(1) - 1 = 3(1) - 1 = 3 - 1 = 2
a(3) = 3a(2) - 1 = 3(2) - 1 = 6 - 1 = 5
a(4) = 3a(3) - 1 = 3(5) - 1 = 15 - 1 = 14
Step 2: Continue the pattern using the recursive rule until we find the 5th term.
a(5) = 3a(4) - 1 = 3(14) - 1 = 42 - 1 = 41
Therefore, the 5th term of the recursive sequence is 41.
To find the 5th term of the recursive sequence where a(1) = 1 and a(n+1) = 3a(n) - 1, we need to follow these steps:
Step 1: Write down the terms of the sequence.
We start with a(1) = 1, as given in the problem. We can calculate the subsequent terms using the recursive formula a(n+1) = 3a(n) - 1.
a(1) = 1
a(2) = 3a(1) - 1 = 3(1) - 1 = 2
a(3) = 3a(2) - 1 = 3(2) - 1 = 5
a(4) = 3a(3) - 1 = 3(5) - 1 = 14
a(5) = 3a(4) - 1 = 3(14) - 1 = 41
Therefore, the 5th term of this sequence is 41.