Page 8 - 11-Math-6 Sequences and Series
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16.. SQeuqaudenracteisc aEnqduSaetrioienss eeLLeeaarrnn..PPuunnjjaabb
12. Find the nth term of the sequence,
 4 2 ,  7 2 ,  10 2 ,...
ï£ï£¬ 3  ï£ï£¬ 3  ï£ï£¬ 3 
13. If 1 , 1 and 1 are in A.P., show that b = 2ac .
ab c a+c
14. If 1 , 1 and 1 are in A.P, show that the common difference is a - c .
ab c 2ac
6.4 Arithmetic Mean (A.M)
A number A is said to be the A.M. between the two numbers a and b if a, A, b are in A.P.
If d is the common difference of this A.P., then A - a = d and b - A = d.
Thus A - a = b - A
or 2A = a + b
⇒ A =a + b
2
Note: Middle term of three consecutive terms in A.P. is the A.M. between the extreme
terms.
In general ,we can say that an is the A.M. between an-1 and an+1, i.e.,
an = an-1 + an+1
2
Example 1: Find three A.Ms between 2 and 3 2 .
Solution: Let A1, A2, A3 be three A.Ms between 2 and 3 2. Then
2, A1, A2, A3,3 2 are in A.P.
Her=e a1 =2, a5 3 2
Using an =a1 + (n -1)d , we get
a5 = a1 + (5 -1)d
version: 1.1
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