Question

find the middle term of the AP 10, 7, 4......-62​

Answer 1

Answer:

-26

Step-by-step explanation:

First term of the AP = 10

Common difference = d = 7 - 10 = - 3

Last term = - 62

Since,

an = a + (n - 1) × d

∴ - 62 = 10 + (n - 1) × (-3)

⇒ - 62 - 10 = - 3n + 3

⇒ - 72 = - 3n + 3

⇒ - 72 - 3 = - 3n

⇒ 3n = 75

⇒ n = 75/3 = 25

∴ Middle term is (25 + 1)/2 = 13th

So, a13 = a + (13 - 1) × d

∴ a13 = 10 + 12 × (-3)

⇒ a13 = 10 - 36 = - 26

∴ Middle term of the AP is - 26.

Answer 2

Answer:

-26

Step-by-step explanation:an = a + (n - 1) × d

a=10

d=7-10=-3

∴ - 62 = 10 + (n - 1) × (-3)

- 62 - 10 = - 3n + 3

- 72 = - 3n + 3

- 72 - 3 = - 3n

3n = 75

n = 75/3 = 25

∴ (25 + 1)/2 = 13

So, a13 = a + (13 - 1) × d

∴ a13 = 10 + 12 × (-3)

a13 = 10 - 36 = - 26

∴ Middle term of the AP is - 26.