The square of a term in the arithmetic sequence 2, 5, 8, ..., is 2500, What is its position

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A18

B17

C16

D15

Answer:

n^{th term} = a + (n-1)d

X_n = 2 + (n - 1)3

= 2 + 3n - 3

X_n = 3n - 1

X_n² = 2500

(3n - 1)²= 2500

$3n-1=\sqrt{2500}$

$3n-1=50$

$3n=50+1=51$

$n=51/3=17$

Since it is a position of a number we need to consider positive root only

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