Question

In the following AP's fill up the missing terms .. 2) 16 __ __ 31​

Answer 1

Answer:

The missing terms in the sequence are: 16, 21, 26, 31

Step-by-step explanation:

Given sequence is 16, __, __, 31

here, a₁ = 16, a₂ = ?, a₃ = ?, a₄ = 31

common difference (d) = ?

(∵aₓ = a+(x-1)d)

a₄ = a+(4-1)d

⇒31 = 16 + 3d

⇒31 - 16 = 3d

⇒15 = 3d ⇒ d = 15/3 ⇒ d = 5

thus, common difference (d) = 5

so, a₂ = a + (2-1)d

⇒a₂ = 16 + 5

⇒a₂ = 21

now, a₃ = a+(3-1)d

⇒a₃ = 16 + 2d

⇒a₃ = 16 + 2(5)

⇒a₃ = 16 + 10

⇒a₃ = 26

∴ the missing terms are 21, 26

The sequence of A.P is 16, 21, 26, 31.

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