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Question
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
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Solution
The given sequence is `2,2sqrt2, 4 ....`
Here, a = 2 and r = `(2sqrt2)/2 = sqrt2`
Let the nth term of the given sequence be 128.
an = arn - 1
= `2(sqrt2)^("n" - 1) = 128`
= `(2) (2)^((n - 1)/2) = (2)^7`
= `(2)^((n - 1)/2 + 1) = (2)^7`
∴ `("n" - 1)/2 = 6`
= n - 1 = 12
= n = 13
Thus, the 13th term of the given sequence is 128.
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