Question

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

Answer 1

Step-by-step explanation:

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, it will have two middle points ie. 18/2 & 18/2 +1

= 9 and 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 the two middle terms of AP is 9/3