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Question
Verify that the following is an AP, and then write its next three terms.
`sqrt(3), 2sqrt(3), 3sqrt(3),...`
Solution
Here,
a1 = `sqrt(3)`
a2 = `2sqrt(3)`
a3 = `3sqrt(3)`
a2 – a1 = `2sqrt(3) - sqrt(3) = sqrt(3)`
a3 – a2 = `3sqrt(3) - 2sqrt(3)= sqrt(3)`
∵ a2 – a1 = a3 – a2 = `sqrt(3)`
Since, difference of successive terms are equal,
Hence, `sqrt(3), 2sqrt(3), 3sqrt(3),...` is an AP with common difference `sqrt(3)`
Therefore, the next three term will be,
a4 = a1 + 3d
= `sqrt(3) + 3(sqrt(3))`
= `4sqrt(3)`
a5 = a1 + 4d
= `sqrt(3) + 4sqrt(3)`
= `5sqrt(3)`
a6 = a1 + 5d
= `sqrt(3) + 5sqrt(3)`
= `6sqrt(3)`
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