the sum of first n consecutive odd integers is n ^ 2. what is the sum of all odd integers between 13 and 31 inclusive.  Choices: A) 220 B) 364 C) 410 D) 424 E) 450
<gadget id="calculator">31 + 1</gadget>
<output>32</output>

<gadget id="calculator">32 / 2</gadget>
<output>16</output>

<gadget id="calculator">16 ** 2</gadget>
<output>256</output>

<gadget id="calculator">13 - 2</gadget>
<output>11</output>

<gadget id="calculator">11 + 1</gadget>
<output>12</output>

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>

<gadget id="calculator">256 - 36</gadget>
<output>220</output>

<result>A</result>
the sum of first n consecutive odd integers is n ^ 2. what is the sum of all odd integers between 13 and 31 inclusive.
subtract(power(divide(add(31, const_1), 2), const_2), power(divide(add(subtract(13, 2), const_1), 2), 2))
we ' re dealing with a sequence of consecutive odd integers : 13 to 31 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 31 = 44 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 29 = 44 now we have proof that there is no middle term . we have 5 bunches of 44 5 ( 44 ) = 220 a