Question

In the following AP's fill up the missing terms .. 4) __, 7 __, __ 1​

Answer 1

Answer:

The missing terms in the sequence of A.P are 9, 7, 5, 3, 1

Step-by-step explanation:

Given that,

the sequence of A.P is __, 7, __, __, 1

Here, a₁ = ?, a₂ = 7, a₃ = ?, a₄ = ?, a₅ = 1

common difference (d) = ?

(∵aₓ = a+(n-1)d )

so, a₂ = a+(2-1)d

⇒ 7 = a+d ↔ (1)

a₅= a+(5-1)d

⇒1 = a+4d ↔ (2)

now, subtract (1) from (2)

⇒eq.(1) - eq.(2)

⇒ 7-1 = a+d - (a+4d)

⇒ 6 = a+d-a-4d

⇒ 6 = -3d

⇒ d = -2

thus, common difference (d) = -2

By substituting d = -2 in eq.(1) we get,

⇒7 = a+d

⇒7 = a-2

⇒a = 7 + 2 = 9

⇒ a = a₁ = 9

So,

a₃ = a + (3-1)d

⇒ a₃ = 9 + 2(-2)

⇒ a₃ = 9 - 4

⇒ a₃ = 5

a₄ = a + (4-1)d

⇒ a₄ = a+3d

⇒ a₄ = 9+3(-2)

⇒ a₄ = 9 - 6

⇒ a₄ = 3

∴ the missing terms are 9, 5, 3

the sequence of A.P is 9, 7, 5, 3, 1