Question

For each positive integer n, the mean of first n terms of sequence is n. What is 2018th term, of the
sequence?

Answer 1

Answer:

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Step-by-step explanation:

Start by determining the first few terms to see if there is a pattern, as there often is in sequence questions:

1st term: n = 1 1+(−1)n1+(−1)n → 1+(−1)11+(−1)1 → 1 + –1 → 0

2nd term: n = 2 1+(−1)n1+(−1)n → 1+(−1)21+(−1)2 → 1 + 1 → 2

3rd term: n = 3 1+(−1)n1+(−1)n → 1+(−1)31+(−1)3 → 1 + –1 → 0

4th term: n = 4 1+(−1)n1+(−1)n → 1+(−1)41+(−1)4 → 1 + 1 → 2

As you can see, all odd terms result in 0, while all even terms result in 2. So only the even terms will count in the sum:

1st 2nd 3rd 4th 5th 6th 7th ...

0 2 0 2 0 2 0 ...

How many even numbers from 1 to 39? 19

Thus the sum = 19×2=3819×2=38

Quantity B is greater.