Question

The nth term of the A.P. 6, 11, 16, 21, ........ is 106, then the value of n – 4 is ______.

Options

• 17

• 15

• 16

• 20

Answer 1

The nth term of the A.P. 6, 11, 16, 21, ........ is 106, then the value of n – 4 is 17.

Explanation:

Let a be the first term and d be the common difference of given A.P.

Here a = 6; d = 11 – 6 = 5

We know that

T_n = a + (n – 1)d

`\implies` 106 = 6 + (n – 1)5

`\implies` 106 – 6 = (n – 1)5

`\implies` 100 = (n – 1)5

`\implies` n – 1 = `100/5` = 20

`\implies` n = 21

Thus, n – 4 = 21 – 4 = 17