Multiple choice

$8^{th}$ term of series $\displaystyle 2\sqrt{2}+\sqrt{2}+0+......$ will be

  1. $\displaystyle -5\sqrt{2}$
  2. $\displaystyle 5\sqrt{2}$
  3. $\displaystyle 10\sqrt{2}$
  4. $\displaystyle -10\sqrt{2}$
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A Correct answer
Explanation

This is an arithmetic progression with first term a = 2*sqrt(2) and common difference d = -sqrt(2). The n-th term is a + (n-1)d. For n = 8, term = 2*sqrt(2) + 7*(-sqrt(2)) = -5*sqrt(2).

AI explanation

The given series 2sqrt(2), sqrt(2), 0 is an arithmetic progression with the first term a = 2sqrt(2) and common difference d = -sqrt(2). The nth term of an arithmetic progression is found using the formula T = a + (n-1)d. For the 8th term, we calculate 2sqrt(2) + (8-1)(-sqrt(2)), which simplifies to 2sqrt(2) - 7sqrt(2). The result is -5sqrt(2).

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