Find the 2nd term of an arithmetic sequence with t5 = 3 and t7 = 7?

Expert Answers

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The nth term of an arithmetic sequence is defined as:

`a_(n) = a + (n - 1)d`

d represents the common difference.  Since the 5th term = 3 and the 7th term = 7, the common difference = 2.

In this case, to find the 2nd term, subtract 2, t4 = 1, t3 = -1, so t2 = -3

To use formula:  find the first term a by substituting a term that is given to find a.

3 = a + (5-1)2  By substituting the 5th term = 3.

3 = a + 8

a = -5  Now use this to find 2nd term by plugging in to equation.

`a_(n) = -5 + (2 - 1)2`

`a_(n) = -5+2`

So the 2nd terms is -3.

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