find the arthematic mean of 1 2 3..... n
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Answer:
⇒ We have the sequence, 1,2,3.......n
⇒ This is an AP, with the initial term a=1 and the common difference d=1.
∴ The sum of n terms of an AP is given by,
⇒ S
n
=
2
n
[2a+(n−1)d]
⇒ S
n
=
2
n
[2×1+(n−1)×1]
⇒ S
n
=
2
n
[2+(n−1)]
⇒ S
n
=
2
n
[n+1]
→ Arithmetic mean of n numbers a
1
,a
2
,a
3
,a
4
,...a
n
is given by the formula
⇒ Arithmeticmean=
n
a
1
+a
2
+a
3
+a
4
+...+a
n
⇒ Arithmeticmean=
n
S
n
⇒ Arithmeticmean=
n
2
n
[n+1]
∴ Arithmeticmean=
2
n+1
Step-by-step explanation:
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