Find the 6th term from end of the A.P. 17, 14, 11,….., (-40).

We know that,

n^th term of an A.P. is given by,

a_n = a + (n - 1)d

Given,

a = 17

d = 14 - 17 = -3

Let no. of terms be n.

⇒ a_n = -40

By formula,

⇒ a_n = a + (n - 1)d

⇒ -40 = 17 + (n - 1)(-3)

⇒ -40 - 17 = (n - 1)(-3)

⇒ -57 = (n - 1)(-3)

⇒ $\dfrac{-57}{-3}$ = n - 1

⇒ 19 = n - 1

⇒ n = 19 + 1

⇒ n = 20.

There are 20 terms in the A.P.

The 8th term from end of the A.P. = 20 - 5 = 15

⇒ a₁₅ = 17 + (15 - 1)-3

= 17 + (14)-3

= 17 - 42

= -25

Hence, the 6th term from end of the A.P is -25.