# arithmetic

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the sum of the 4th and 8th terms is 10, and the sum of the 6th and 12th terms is 22. Find the first three terms.

• arithmetic -

a + 3d + a + 7d = 10
2a + 10d = 10
a + 5d = 5

a+5d + a+11d = 22
2a + 16d = 22
a + 8d = 11

subtract them
3d = 6
d = 2
back into the first
a + 5d = 5
a + 10 = 5
a = -5

first 3 terms are -5, -3, -1

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