Multiple choice

What is the sum of the first nineteenth terms of the arithmetic sequence 2, 6, 10, 14.....?

  1. $522$
  2. $622$
  3. $722$
  4. $822$
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C Correct answer
Explanation

Arithmetic sequence: a = 2, d = 4. Sum of n terms = n/2 * (2a + (n-1)d). For n = 19: 19/2 * (2*2 + 18*4) = 19/2 * (4 + 72) = 19/2 * 76 = 19 * 38 = 722.

AI explanation

Apply the arithmetic series sum formula Sn = n/2 * (2a + (n-1)d). The first term a is 2, the common difference d is 4 (6 - 2), and the number of terms n is 19. Substituting these values gives S19 = 19/2 * (2*2 + (19-1)*4) = 19/2 * (4 + 72) = 19/2 * 76 = 19 * 38 = 722.

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