The twenty-third term in an arithmetic sequence is and the fifty-third term in the sequence is . What is the thirty-fifth te

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The twenty-third term in an arithmetic sequence is $\frac23$ and the fifty-third term in the sequence is $\frac32$ . What is the thirty-fifth term?

Guest Jan 17, 2015

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Best Answer

The formula for the n^th term of an arithmetic sequence is: t_n = a + (n - 1)d

---> 2/3 = a + 22d

---> 3/2 = a + 52d

Subtracting the top equation from the bottom equation: 5/6 = 30d ---> d = 1/36

Multiplying the top equation by 52: 104/3 = 52a + 1144d

Multiplying the bottom equation by -22: -33 = -22a - 1144d

Adding down: 5/3 = 30a ---> a = 1/18

To find the 35th term: value = 1/18 + (35 - 1)(1/36) <--- the answer.

geno3141 Jan 17, 2015

geno3141 · Answer 1 · 2015-01-17T07:17:12