Question

Find the sum of two middle most terms of AP: -4/3,-1,-2/3,.......13/3

Answer 1

To find the two most middle most terms of AP, we have to find the number of terms in the AP. There is a common difference between each term of arithmetic progression which is termed as 'd'
i.e (-4/3)+d=-1
=> d=-1+(4/3)
=> d=1/3
The formula is
an=a1+(n-1)d
an is the nth term of AP
a1 is the first term of AP
n is number of terms
by substituting an=13/3,a1=-4/3,d=1/3
we get n=18
So the AP has 18 terms whose two middle most terms are 9th and 10th terms.
By substituting n=9 and d=1/3 in the formula, we get 9th term of AP which is 4/3
By substituting n=10 and d=1//3 in the formula, we get 10th term of AP which is 5/3

Answer 2

The Ap is..

-4/3,-1,-2/3...13/3

Common difference d = a2 -a1 = -1 - (-4/3)

d = -1+ 4/3=1/3

Number of terms in the AP =n

We know that last term of AP

an= a1 + (n-1)d

an=13/3 a1=-4/3

so.....

13/3 = -4/3 + (n-1)(1/3)

13/3 + 4/3 = (n-1)/3

17/3=(n-1)/3

17=n-1

n=18

as n is equal to 18..... so it will have two middle points ie. 18/2 & 18/2 +1

=9 & 10

so we have to find sum of 9th and 10th term of AP`

a9 +a10 = [a1 +(9-1)(1/3)] + [a1+ (10-1)(1/3)]

a9 + a10 =-4/3 +8/3 + (-4/3) +9/3

a9 + a10 =9/3

So the sum of middle terms of AP is 9/3