# Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .?

2n - 1, n, n + 2, 2n

**Solution:**

It is given that

The sequence that is given to us is 1, 3, 5, 7, 9, ...

**Let us assume a _{1} = 1, a_{2} = 3, a_{3} = 5, a_{4} = 7, a_{5} = 9**

Then,

a_{2}_{ }- a_{1 } = 3 - 1 = 2

a_{3} - a_{2} = 5 - 3 = 2

a_{4} - a_{3} = 7 - 5 = 2

a_{5} - a_{4} = 9 - 7 = 2.

**Hence, from the above simplification we can see that the common difference is 2.**

**So, the nth term of an arithmetic progression whose first term a _{1} = 1 and common difference d = 2 is given by,**

a_{n} = a_{1} + (n - 1) d

**Substituting the values:**

a_{n }= 1 + (n - 1) 2

= 1 + 2n - 2

= 2n - 1

**Therefore, the general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.**

## Which of the following represents the general term for the sequence 1, 3, 5, 7, 9, . . .?

2n - 1, n, n + 2, 2n

**Summary:**

The general term for the sequence 1, 3, 5, 7, 9, . . . is 2n - 1.

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