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Algebra2 Selection of Terms in an A.P.
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Selection of Terms in an A.P.
Sometimes we require certain number of terms in A.P. The following ways of selecting terms are generally very convenient.

Number of Terms Terms Common Difference
3 a-d, a, a+d d
4 a-3d, a-d, a+d, a+3d 2d
5 a-2d, a-d, a, a+d, a+2d d
6 a - 5d, a - 3d, a - d, a + d, a + 3d, a + 5d 2d

It should be noted that in case of an odd number of terms, the middle term is a and the common difference is d while in case of an even number of terms the middle terms are a -d,a + d and the common differences is 2d.
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Example: The sum of three numbers in A.P is -6, and their product is 24. Find the numbers.
Solution: Let the numbers be (a - d), a, (a+d). Then,
Sum = -6 (a-d) + a + (a+d) = -6 3a = -6 a = -2
Product = 24 (a - d) (a) (a + d) = 24
a(a2-d2) = 24
(-2)(4 - d2 ) = 24                   ...[a = -2]
d2 = 16 = 4
If d = 4, the numbers are - 6, - 2, 2. If d = - 4, the numbers are 2, - 2, - 6.
Thus, the numbers are -6,-2, 2, or 2, - 2, -6.
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