Question

Arith matic mean of the series 1,3,5.... (2 n - 1) is​

Answer 1

Answer:

the number 1,3,5, ..........(2n-1) is n.

Step-by-step explanation:

To find : The arithmetic mean of the number 1,3,5, ..........(2n-1) ?

Solution :

The arithmetic mean is defined as sum of first term and last terms divided by 2 i.e. AM=\frac{a+b}{2}AM=

2

a+b

Here, a=1 and b=2n-1

Substitute the value,

AM=\frac{1+2n-1}{2}AM=

2

1+2n−1

AM=\frac{2n}{2}AM=

2

2n

AM=nAM=n

Therefore, the arithmetic mean of the number 1,3,5, ..........(2n-1) is n.

Step-by-step explanation:

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Answer 2

Answer:

Arithmetic Mean = n

Step-by-step explanation:

AP : 1, 3, 5, ...................., (2n-1)

a = 1

d = 2

Sn = n/2( a + l )

Sn = n/2( 1 + 2n - 1 ) = n²

Arithmetic mean = Sn/n = n²/n = n