Question

The AM of 10 consecutive numbers starting with n+1​

Answer 1

Answer:

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Answer 2

Given,

10 consecutive numbers starting with (n+1).

To find,

The arithmetic mean.

Solution,

The arithmetic mean of 10 consecutive numbers starting with (n+1) will be (n + 11/2).

We can easily solve this problem by following the given steps.

According to the question,

10 consecutive numbers are starting with (n+1).

(n+1), (n+2), (n+3), ---, (n+10)

So, this series becomes an AP with the same difference between the two consecutive terms.

Common difference(d) = second term -first term

d = (n+2)-(n+1)

d = 1

The first term (a) = (n+1)

The last term (l) = (n+10)

Now, we know that the formula to find the arithmetic mean is given as follows:

Mean = Sum of all the observations/total number of observations

Sum of all observations = Sum of 10 terms of AP

The formula to find the sum of n terms in an AP is given as follows:

Sn = n/2 (a+l) where n is the number of terms

S10 = 10/2 (n+1+n+10)

S10 = 5(2n+11)

Mean = Sum of all the observations/total number of observations

Mean = 5(2n+11)/10

Mean = (2n+11)/2

Mean = (n + 11/2)

Hence, the arithmetic mean of 10 consecutive numbers starting with (n+1) is (n + 11/2).