Answer: 373
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Explanation:
The sequence {1,2,3,4,1,2,3,4...} has "1,2,3,4" repeat forever. We can say that the cycle is 4 terms before it restarts the pattern again. Because of this 4-cycle pattern, we know that 150/4 = 37.5 = 37 full cycles happen. The leftover part is of length 150-37*4 = 2.
In short we have 37 full cycles of {1,2,3,4} happening. The last leftover bit has {1,2} only
In the subsquence {1,2,3,4} its sum is 1+2+3+4 = 10. Having 37 copies of {1,2,3,4} leads to a sum of 37*10 = 370 so far.
Then we add on the last bit 1+2 = 3 to get 370+3 = 373.
Therefore, the sum of the first 150 terms is 373. I think your teacher made a typo when listing out the answer choices. Please double check to make sure.
