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the sum of the 3rd and the 4th term is 44 and the sum of the 10th and the 15th term is 203. what is the sum up to the 20th term?

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I assume you are referring to an arithmetic sequence.

a+2d + a+3d = 44
a+9d + a+14d = 203

2a + 5d = 44
2a + 23d = 203

18d = 159
d = 159/18
a = -1/12

S20 = 20/2(T1+T20)
= 167.75

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