Question

Find the sum of two middle most terms of AP -4/3, -1, -2/3,........., 4 1/3. {Ans. - 3}

Answer 1

Answer:

3

Step-by-step explanation:

Given, First term a = -4/3.

Common difference = -1 + 4/3

                                   = 1/3

nth term = a(n) = 13/3.

∴ nth term of an AP = a + (n - 1) * d

⇒ 13/3 = -4/3 + (n - 1) * 1/3

⇒ 13/3 + 4/3 = (n - 1) * 1/3

⇒ 17/3 = (n - 1)/3

⇒ 17 = (n - 1)

⇒ n = 18

∴ So,the given ap contains 18 terms. The middle terms are (n/2), (n/2) + 1.

= (18/2), (18/2) + 1

= 9,10

Sum of two middle terms:

= 9th term + 10th term

= [a + (9 - 1) * d] + [a + (10 - 1) * d]

= [a + 8d] + [a + 9d]

= [-4/3 + 8(1/3)] + [-4/3 + 9(1/3)]

= [-4/3 + 8/3] + [-4/3 + 3]

= -4/3 + 8/3 - 4/3 + 3

= -8/3 + 8/3 + 3

= 3.

Therefore,Sum of two middle most terms is 3.

Hope it helps!

Answer 2

Answer:

3

Step-by-step explanation:

Given, First term a = -4/3.

Common difference = -1 + 4/3

                                  = 1/3

nth term = a(n) = 13/3.

∴ nth term of an AP = a + (n - 1) * d

⇒ 13/3 = -4/3 + (n - 1) * 1/3

⇒ 13/3 + 4/3 = (n - 1) * 1/3

⇒ 17/3 = (n - 1)/3

⇒ 17 = (n - 1)

⇒ n = 18

∴ So,the given ap contains 18 terms. The middle terms are (n/2), (n/2) + 1.

= (18/2), (18/2) + 1

= 9,10

Sum of two middle terms:

= 9th term + 10th term

= [a + (9 - 1) * d] + [a + (10 - 1) * d]

= [a + 8d] + [a + 9d]

= [-4/3 + 8(1/3)] + [-4/3 + 9(1/3)]

= [-4/3 + 8/3] + [-4/3 + 3]

= -4/3 + 8/3 - 4/3 + 3

= -8/3 + 8/3 + 3

= 3.

Therefore,Sum of two middle most terms is 3.

Hope it helps!