Find the sum of natural number from 1 to 30

nth term of an arithemetic sequence 20,50,80, ...

write the algebric form

write the sequence of natural numbers term in the above sequence

1. sum of term = 465

2. nth term of the AP = 30n - 10

Step-by-step explanation:

1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1. Therefore

sum of term = n/2 (a + l)

where

a = 1

l = last term = 30

n = number of term

sum of term = 30/2 (1 + 30)

sum of term = 15 (31)

sum of term = 465

2. The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ...

The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;

a = 20

d = 30

nth term of an AP = a + (n - 1) d

nth term of an AP = 20 + (n - 1) 30

nth term of an AP = 20 + 30n - 30

nth term of the AP = 30n - 10

The nth term formula can be used to find the next term progressively. where n = number of term

The sequence will be 20, 50, 80, 110, 140, 170, 200 ...