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प्रश्न
Which of the following sequences are A.P.? If they are A.P. find the common difference.
`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2, ...`
उत्तर
t2 − t1 = `3 + sqrt2 - 3 = sqrt2`
t3 − t2 = `3 + 2sqrt2 - (3 + sqrt2)`
= `3 + 2sqrt2 - 3 - sqrt2`
= `sqrt2`
t4 − t3 = `3 + 3sqrt2 - (3 + 2sqrt2)`
= `3 + 3sqrt2 - 3 - 2sqrt2`
= `sqrt2`
∵ The difference between consecutive terms are same.
∴ Given sequence is an A.P.
Common difference (d) = `sqrt2`
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