find the 8th term of the sequence defined by the given rule:
f(1)=5
f(n)=f(n-1)+2
f(1) = 5
f(2) = f(1) + 2 = 7
f(3) = f(2) + 2 = 9
....
keep going
or , it looks like
f(n) = 2n + 3
f(8) = 16+3 = 19
To find the 8th term of the given sequence, you can use the recursive rule provided.
Given:
f(1) = 5, and
f(n) = f(n-1) + 2
To find the 8th term, we need to calculate f(8) using the recursive rule.
f(2) = f(1) + 2 = 5 + 2 = 7
f(3) = f(2) + 2 = 7 + 2 = 9
f(4) = f(3) + 2 = 9 + 2 = 11
f(5) = f(4) + 2 = 11 + 2 = 13
f(6) = f(5) + 2 = 13 + 2 = 15
f(7) = f(6) + 2 = 15 + 2 = 17
f(8) = f(7) + 2 = 17 + 2 = 19
Therefore, the 8th term of the sequence is 19.
To find the 8th term of the sequence defined by the given rule, we need to apply the recurrence relation:
f(1) = 5
f(n) = f(n-1) + 2
To find f(2), we substitute n = 2 into the recurrence relation:
f(2) = f(2-1) + 2
f(2) = f(1) + 2
f(2) = 5 + 2
f(2) = 7
To find f(3), we substitute n = 3 into the recurrence relation:
f(3) = f(3-1) + 2
f(3) = f(2) + 2
f(3) = 7 + 2
f(3) = 9
We continue this process until we reach the 8th term:
f(4) = f(4-1) + 2
f(4) = f(3) + 2
f(4) = 9 + 2
f(4) = 11
f(5) = f(5-1) + 2
f(5) = f(4) + 2
f(5) = 11 + 2
f(5) = 13
f(6) = f(6-1) + 2
f(6) = f(5) + 2
f(6) = 13 + 2
f(6) = 15
f(7) = f(7-1) + 2
f(7) = f(6) + 2
f(7) = 15 + 2
f(7) = 17
f(8) = f(8-1) + 2
f(8) = f(7) + 2
f(8) = 17 + 2
f(8) = 19
Therefore, the 8th term of the sequence is 19.