Question

Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers but no even number

Answer 1

Given: First term 1/3 and Common Difference 2/3

To find: Prove that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers but no even number.

Solution:

• Now we have given first term as 1/3 and common difference ad 2/3.

• Now Arithmetic Progression is:

                   a, a + d, a + 2d, a + 3d .........

• Here a = 1/3 and d = 2/3.

• So putting the values, we get:

                   1/3, 1/3 + 2/3, 1/3 + 2(2/3), 1/3 + 3(2/3), ........

                   1/3, 1, 5/3, 7/3, ..........

• So this is the arithmetic progression formed where no even number is found.

Answer:

              So from solution part, we proved that the arithmetic sequence with first term 1/3 and common difference 2/3 contains all odd numbers.

Answer 2

Answer:

a=1/3 d= 2/3

a-d = 1/ 3- 2/3 =-1/3

n= 2 4-1 ÷3 = 9/3=3 ✔

+3

n=5