Question

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

Answer 1

Solution:-
There is a mistake in this question. The first term should be - 4/3 instead of 
- 4, otherwise the common difference will not be equal.
The AP with the first term is- 4/3 and the last term is 13/3.
The nth term of the AP is given by a + (n - 1)d = Tn. Here a is the first term and d is the common difference.
Tn is the last term.
d = Tn + 1 - Tn, here n is the natural number.
So, d = - 1 - (-4/3)
common difference = 1/3
So, using this formula ----- a + (n - 1)d = Tn  we get
⇒ - 4/3 + (n - 1)1/3 = 13/3
⇒ (-5 +n)/3 = 13/3
3n = 39 + 15
3n = 54
n = 18
So, there are 18 terms in the given AP.
The two middle most terms are 9th term and 10th term.
Hence, T₉ = - 4/3 + (9 - 1)1/3 
T₉ = 4/3
T₁₀ = - 4/3 + (10 - 1)1/3
T₁₀ = 5/3
So, sum of the two middle most terms of the given AP = 4/3 + 5/3
= 9/3
= 3
Answer

Answer 2

hope it will help you