Algebra2 Selection of Terms in an A.P.
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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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