Verify that √3 , 2√3, 3√3,…is an AP, and then write its next t

1.	Verify that √3 , 2√3, 3√3,…is an AP, and then write its next three terms.
Answer» Here, a₁= √3 a₂ = 2√3 a₃ = 3√3 a₄ = 4√3 a₂ – a₁ = 2√3 – √3 = √3 a₃ – a₂ = 3√3 – 2√3= √3 a₄ – a₃ = 4√3 – 3√3= √3 Since, difference of successive terms are equal, Hence, √3 , 2√3, 3√3,… is an AP with common difference √3. Therefore, the next three term will be, 4√3 + √3, 4√3 + 2√3, 4√3 + 3√3 5√3, 6√3, 7√3

Verify that √3 , 2√3, 3√3,…is an AP, and then write its next three terms.

Answer»

Here,

a₁= √3

a₂ = 2√3

a₃ = 3√3

a₄ = 4√3

a₂ – a₁ = 2√3 – √3 = √3

a₃ – a₂ = 3√3 – 2√3= √3

a₄ – a₃ = 4√3 – 3√3= √3

Since, difference of successive terms are equal,

Hence, √3 , 2√3, 3√3,… is an AP with common difference √3.

Therefore, the next three term will be,

4√3 + √3, 4√3 + 2√3, 4√3 + 3√3

5√3, 6√3, 7√3