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Write down the series whose r^(th) term ...

Write down the series whose `r^(th)` term is` 3. 2 ^(r + 1 ) `. Is it a geometric series ?

Text Solution

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Given, `a_(r) = 3. 2^(r + 1)`
Putting r = 1, 2, 3, … we get
`a_(1) = 3 xx 2^(2) = 12 `
`a_(2) = 3 xx 2^(3) = 24 `
` a_(3) = 3 xx 2^(4) = 48 `
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`therefore ` The series is ` 12 + 24 + 48 + …`
Here, `(a_(2))/(a_(1)) = (a_(3))/(a_(2)) = ... = 2 `
`therefore ` The series is a geometric series with common ratio = 2
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