Question

The formula for an arithmetic series is shown below, where n = 1, 2, 3 ...

Answer 1

Answer:

4th term = 28

5th term =  37

6th term = 45

Step-by-step 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.