Multiple choice

In an arithmatic series, the 3rd term is 15 whereas the 15th term is 51. What is the sum of first 10 terms of the series?

  1. 145

  2. 160

  3. 180

  4. 225

  5. 210
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D Correct answer
Explanation

The difference between the 15th and 3rd terms is 12d, so 12d = 36 and d = 3. Then a = 9, and the sum of the first 10 terms is 10/2 x (2(9) + 9(3)) = 225.

AI explanation

For an arithmetic series, the nth term is given by the formula a plus (n minus 1) times d. Using the given values, the third term 15 equals a plus 2d, and the 15th term 51 equals a plus 14d. Solving these two equations yields the first term a as 9 and the common difference d as 3. The sum of the first 10 terms is found using the formula S equals n divided by 2 multiplied by (2a plus (n minus 1)d), which calculates to 5 multiplied by 18 plus 27, resulting in 225.

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