Question

Find the sum of two middle terms of the A.P. :

`-4/3, -1, (-2)/3, -1/3, ..., 4 1/3`

Answer 1

Given: A.P. : `-4/3, -1, -2/3, -1/3, ..., 4 1/3`.

Step-wise calculation:

1. First term `a = -4/3`.

Common difference `d = -1 - (-4/3) = 1/3`.

2. Last term `l = 4 1/3 = 13/3`. 

Use a + (n – 1)d = l: `-4/3 + (n - 1)(1/3) = 13/3` 

Multiply by 3: –4 + (n – 1) = 13

n – 1 = 17

n = 18

3. n is even, so the two middle terms are the 9^th and 10^th terms.

a₉ = a + 8d

= `-4/3 + 8(1/3)`

= `4/3`

a₁₀ = a + 9d

= `-4/3 + 9(1/3)`

= `5/3`

4. Sum of the two middle terms = `4/3 + 5/3`

= `9/3`

= 3

The sum of the two middle terms is 3.