Explain in detail, how you solved the following problem: The first two terms of a sequence are 10 and 20. If each term after the second term is the average of all of the preceding terms, what is the 2020th term?

Explanation:

Given

Each term after the second term is the average of all of the preceding terms

Required:

Explain how to solve the 2020th term

Solve the 2020th term

Solving the 2020th term of a sequence using conventional method may be a little bit difficult but in questions like this, it's not.

The very first thing to do is to solve for the third term;

The value of the third term is the value of every other term after the second term of the sequence; So, what I'll do is that I'll assign the value of the third term to the 2020th term

This is proved as follows;

From the question, we have that "..... each term after the second term is the average of all of the preceding terms", in other words the MEAN

Assume n = 3

Multiply both sides by 2

Assume n = 4

Substitute

Assume n = 5

Substitute and

Replace 5 with n

(n-1) will definitely cancel out (n-1); So, we're left with

Hence,

Calculating

Recall that