Question

Find the two middle most term of AP -5/3, -4/3, -1, -2/3,..., 4 2/3

Answer 1

Answer:

Ap is 3

Step-by-step explanation:

Solution:

Given, the arithmetic series is -4/3, -1, -2/3,-------------,4 ⅓

We have to find the sum of the two middle most terms of the series.

From the given series,

First term, a = -4/3,

aₙ = 4 ⅓ = 13/3

Common difference, d = -1 - (-4/3)

= -1 + 4/3

= (-3+4)/3

d = 1/3

The n-th term of an AP is given by

aₙ = a + (n - 1)d

To find n,

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

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

17/3 = (1/3)(n - 1)

n - 1 = 17

n = 17 + 1

n = 18

The two middle most terms of the 18 terms of the series are 9th and 10th terms.

So, a₉ = -4/3 + (9 - 1)(1/3)

= -4/3 + (8/3)

= (-4+8)/3

a₉ = 4/3

a₁₀ = -4/3 + (10 - 1)(1/3)

= -4/3 + (9/3)

= (-4+9)/3

a₁₀ = 5/3

Now, sum of two middle terms = a₉ + a₁₀

= 4/3 + 5/3

= (4+5)/3

= 9/3

= 3

Therefore, the sum of the two middlemost terms of the given AP is 3.