The 8^{th} term of the series 2sqrt{2} + sqrt | vedclass

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(A) The given series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ is an Arithmetic Progression $(A.P.)$.Here,the first term $a = 2\sqrt{2}$ and the common diffe

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$-5$

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(A) The given series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ is an Arithmetic Progression $(A.P.)$.Here,the first term $a = 2\sqrt{2}$ and the common difference $d = \sqrt{2} - 2\sqrt{2} = -\sqrt{2}$.The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d$.For the $8^{th}$ term $(n = 8)$:$a_8 = 2\sqrt{2} + (8 - 1)(-\sqrt{2})$$a_8 = 2\sqrt{2} + 7(-\sqrt{2})$$a_8 = 2\sqrt{2} - 7\sqrt{2}$$a_8 = -5\sqrt{2}$.

The $8^{th}$ term of the series $2\sqrt{2} + \sqrt{2} + 0 + \dots$ will be: (in $\sqrt{2}$)

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