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Answer:
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
<em>This is proved as follows;</em>
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
<em>Assume n = 3</em>
<em>Multiply both sides by 2</em>
<em>Assume n = 4</em>
Substitute
Assume n = 5
Substitute and
<em>Replace 5 with n</em>
<em>(n-1) will definitely cancel out (n-1); So, we're left with</em>
Hence,
Calculating
Recall that