Question

For what value of x will be x+9 2x-1 and 2x+7 are the consecutive terms of an ap

Answer 1

Answer:

The value of x is 18 for which three terms are in AP.

Step-by-step-explanation:

We have given that,

x + 9, 2x - 1 and 2x + 7 are consecutive terms of an AP.

• t₁ = x + 9
• t₂ = 2x - 1
• t₃ = 2x + 7

For three consecutive terms of the AP,

t₂ - t₁ = t₃ - t₂

⇒ 2x - 1 - ( x + 9 ) = 2x + 7 - ( 2x - 1 )

⇒ 2x - 1 - x - 9 = 2x + 7 - 2x + 1

⇒ - 1 - x - 9 = 7 - 2x + 1

⇒ - x - 10 = - 2x + 8

⇒ - x + 2x = 8 + 10

⇒ x = 18

∴ The value of x is 18 for which three terms are in AP.

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Verification:

t₁ = x + 9 = 18 + 9 = 27

t₂ = 2x - 1 = 2 * 18 - 1 = 36 - 1 = 35

t₃ = 2x + 7 = 2 * 18 + 7 = 36 + 7 = 43

Now,

t₂ - t₁ = 35 - 27 = 8

t₃ - t₂ = 43 - 35 = 8

∴ t₂ - t₁ = t₃ - t₂

∴ The three terms are in AP.

Hence verified!