Question

find 11th term from the last term of the AP 27 , 23 , 19 ,..., - 65

Answer 1

We have to find the 11th term from last.

But for that we have to find the number of last term.

For that let Tₙ= -65
Now,

Tₙ= a+(n-1)d

Here Tₙ = -65 ; a = 27 ; d = -4

∴ -65 = 27 + (n-1)(-4)
∴ -92 = (n-1)(-4)
∴ -92 = -4n+4
∴ -96 = -4n
∴ n = 24

Therefore, 24th term is the last term in A.P.

As e have to find the 11th term from last

11th term from last will be (24-11)th term from starting.

That is 13th term from start.

Now we have to find the 13th term of AP

∴ Tₙ= a+(n-1)d
∴ T₁₃ = 27 +(13-1)(-4)
∴ T₁₃ = 27 +12(-4)
∴ T₁₃ = 27 - 48
∴ T₁₃ = -21

Answer:- 11th term from the last in AP is -21