Question

Find the 15th term from the last term of the Ap 11,8,5,etc last term -64

Answer 1

I hope you are satisfied

Answer 2

Given:

An A.P. series,

$11,8,5...(-64)$

To find:

$15_{th}$ term from the end of A.P.

Solution:

We have been given the A.P. series whose

First term (a) = 11 ;and

Last term (l) = -64

Common difference (d) will be,

d = a₂ - a₁ = 8 - 11 = -3

Hence, d = -3

To find the total number of terms in the A.P. , we have the relation for

$n_{th}$ term of the series $= a +(n- 1)d$

Hence, substituting the known values in the equation, we get

$(-64)= 11+(n-1)(-3) ;\\n-1=25$

$or$

$n=26$

Hence, total number of terms in the series is 26 and

We have to find $15_{th}$ term from the end,

Now, we see that

START    |<------- 11-------->(12th / 15th)<-----------14---------->|     END

In the above representation, we see, clearly that the 15th term from the end of the A.P. will be the 12th term from the beginning .

Hence,

$a_{12} = a+((12-1)d)$  ; or

$a_{12} = 11+11(-3)$ ;or

$a_{12} = -22$

Final answer:

Hence, the $15_{th}$ term from the end of the A.P. will -22 .