Question

What are the middle most terms of the A.P. -11,-7,-3,…..49?

Answer 1

in the given AP

First term        a = -11
 last term         A = 49
difference        d = 4

Thus formula for Last term

A = a + (n-1)d
 49 = -11 + (n-1) 4
49+11 = 4n-4
 4n = 64
n= 16

Thus the number of terms = 16
So middle most term is 8th term

A(8) = a + (8-1)d
        = -11 + 7*4
        = 28 - 11
        =  17
thus middle most term is 17

Answer 2

Given A.P is
-11,-7,-3,…..49
We have to calculate the middle most term of the series.
Here,
a = -11
A = 49
d = -7 + 11 = 4
First we calculate the total number of terms by using the formula:
A = a + (n-1) d   .......... (1)
Putting the values, we get:
49 = -11 + (n-1) 4
49 + 11 = 4n - 4
60 = 4n - 4
60 + 4 = 4n
64 = 4n
n = 16
So, total No. of terms = 16
Middle most term = 16/2 = 8
Put n=8 in equation (1) :
A₈ = -11 + (8-1) 4
A₈ = -11 + (7) 4
A₈ = -11 + 28
A₈ = 17
which shows that the middle most term is 17
This is the required answer.
Thanks.