Answer:
4th term = 28
5th term = 37
6th term = 45
Explanation:
f(n + 1) = f(n) + 8
f(1) = 5
f(1 + 1) = f(1) + 8 = 5+8 = 13
f(2) = 13
f(2 + 1) = f(2) + 8 = 13+8 = 21
Thus, series is 5, 13, 21......
In arithmetic series
Nth term is given by
n th term = a + (n-1)d
where a is the first term
and d is the common difference.
common difference d = nth term - (n-1)th term
For this series
a = 5
lets take nth term as 2nd term and 1st term as (n-1)th term
d = 13-5 = 8
n th term = a + (n-1)d
using the formula for nth term
4th term = 5 + (4-1)8 = 29
5th term = 5 + (5-1) 8= 37
6th term = 5+ (6-1)8 = 45
Thus, 4th term = 28
5th term = 37
6th term = 45
Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.