Arithmetic Mean:
- If three terms are in A.P., then the middle term is known as the arithmetic mean (A.M.) between the other two i.e. if a,b,c are in A.P. then b=a+c/2 is the A.M. of a and c.
- If a1, a2, ...an are n numbers then the arithmetic mean (A) of these numbers is
- The n numbers A1, A2......An are said to be A.M's between the numbers b and a if a, A1, A2,........An,b are in A.P. If d is the common difference of that A.P. then
.
Problem: If the Ist and the 2nd terms of an A.P are 1 and -3 respectively, calculate the nth term and the addition of the Ist n terms.
Solution: Ist term = a, 2nd term = a + d where a = 1, a + d = -3,
Þ d = -4 (Common difference of A.P.)
we have an = a + (n -1)d
= 1 + (n - 1) (-4) = 5 - 4n
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