Question

n^th term of the A.P.: `(-1)/3, 4/3, 3,` ... is ______.

विकल्प

• `(5n - 9)/3`

• `(5n - 6)/3`

• `(3n - 4)/3`

• `(3n + 2)/3`

Answer 1

n^th term of the A.P.: `(-1)/3, 4/3, 3,` ... is `underlinebb((5n - 6)/3)`.

Explanation:

The n^th term of an arithmetic progression (A.P.) is given by:

a_n = a + (n – 1)d

where:

a is the first term

d is the common difference

Given:

`a = - 1/3`

`d = 4/3 - (- 1/3)`

= `4/3 + 1/3`

= `5/3`

So, `a_n = -1/3 + (n - 1) xx 5/3`

= `- 1/3 + (5n - 5)/3` 

= `(-1 + 5n - 5)/3`

= `(5n - 6)/3`