Question

Find the common difference d and write next 3 terms for the √2, √8, √18, √32

Answer 1

Answer:

Given AP = √2, √8, √18, √32, ...

We can simplify and write the values as:

• √8 = √ ( 4 × 2 ) = 2√2
• √18 = √ ( 9 × 2 ) = 3√2
• √32 = √ ( 16 × 2 ) = 4√2

Hence the AP is: √2, 2√2, 3√2, 4√2, ...

Common difference is : ( a₂ - a₁ ) = 2√2 - √2 = √2

Hence the common difference is √2.

Hence the next three terms after 4√2 ( √32 ) are:

⇒ 4√2 + √2 = 5√2 = √50

⇒ 5√2 + √2 = 6√2 = √72

⇒ 6√2 + √2 = 7√2 = √98

Hence the next three terms are: √50, √72, √98.

Answer 2

Common differences d=
$\sqrt{8 } - \sqrt{2} = \sqrt{18 } - \sqrt{8 } = \sqrt{2}$
Next three terms are=
$\sqrt{50} \: \: \: \: \: \: \: \: \sqrt{72} \: \: \: \: \: \: \: \: \sqrt{98}$