Question

If `(-20)/9, (-2)/9, 16/9,` .... are in A.P., then next term of the sequence is ______.

Options

• `32/9`

• `46/9`

• `2/9`

• `34/9`

Answer 1

If `(-20)/9, (-2)/9, 16/9,` .... are in A.P., then next term of the sequence is `underlinebb(34/9)`.

Explanation:

1. Find the common difference (d)

In an A.P., the common difference is found by subtracting any term from the term that follows it:

d = Term₂ – Term₁

`d = - 2/9 - (- 20/9)`

`d = - 2/9 + 20/9`

`d = 18/9`

d = 2

To verify, let’s check the difference between the second and third terms:

`16/9 - (- 2/9) = 16/9 + 2/9`

= `18/9`

= 2

2. Calculate the next term

To find the next term (the 4th term), add the common difference `(d = 18/9)` to the 3rd term:

Next term = `16/9 + 18/9`

Next term = `34/9`