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Suppose A is the first term and R is common difference.

Then, if t(n) is the nth term,

t(n) = A + n*R

Then

t(5) = A + 5R

and

t(3) = A + 3R

so that

t(5) - t(3) = 2R

Now t(1) = A + R = A + 3R - 2R (since R = 3R - 2R)

So t(1) = t(3) - 2R

You were given t(3) and have calculated 2R above, so can work out t(1).

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12y ago
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Q: How can you find the first term of an arithmetic sequence if you know the third and fifth terms?
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