Question

For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?

Answer 1

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Answer 2

Answer: 4015

Solution:

Given:

Total number of terms = n

Mean of the first n terms= n

Find:

2008th term of the sequence=?

The formula of mean is given as:

Mean = Sum of n terms/total number of integers...................1

Mean and the total number of integers are already given.

putting the values in equation 1

Sum = Mean * total number of integers

Sum = n*n

Sum  of n terms= n²...................2

the value of the nth term is found by subtracting the sum of  nth term to Sum of (n-1)th term

Taking from equation 2,

Sum of 2008th term = 2008²

Sum of 2007th term = 2007²

Subtracting bot the terms,

2008th term =2008²-2007²

2008th term =4032064 - 4028049

2008th term = 4015

Hence the 2008th term is 4015

#SPJ3