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Ilia_Sergeevich [38]

4 years ago

13

50 POINTS AND BRAINLIEST You don't let Elvis off the hook so easily. His sign obviously says that his eyes are terrible. "Fine,

fine," he says, "I can't see a thing. But didn't anyone else seem fishy?"
Think about every creature that you interviewed. Were there other suspicious answers? Think about a creature that seemed "alarmed" when questioned. *
Oscar
Eelvis
Leonardo
Blue

Advanced Placement (AP)

1 answer:

Bogdan [553]4 years ago

5 0

I feel like it is blue that is sus

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Explanation:

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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

$T_{n} = \frac{\sum T{k}}{n-1} ; where: k = 1 .... n -1$

<em>Assume n = 3</em>

$T_{3} = \frac{T_1 + T_2}{2}$

<em>Multiply both sides by 2</em>

$2 * T_{3} = \frac{T_1 + T_2}{2} * 2$

$2T_{3} = T_1 + T_2$

<em>Assume n = 4</em>

$T_{4} = \frac{T_1 + T_2 + T_3}{3}$

$T_{4} = \frac{(T_1 + T_2) + T_3}{3}$

Substitute $2T_{3} = T_1 + T_2$

$T_{4} = \frac{2T_3 + T_3}{3}$

$T_{4} = \frac{3T_3}{3}$

$T_{4} = T_3$

Assume n = 5

$T_{5} = \frac{T_1 + T_2 + T_3 +T_4}{4}$

$T_{5} = \frac{(T_1 + T_2) + T_3 +(T_4)}{4}$

Substitute $2T_{3} = T_1 + T_2$ and $T_{4} = T_3$

$T_{5} = \frac{2T_3 + T_3 +T_3}{4}$

$T_{5} = \frac{4T_3}{4}$

$T_{5} = \frac{(5-1)T_3}{5-1}$

<em>Replace 5 with n</em>

$T_{n} = \frac{(n-1)T_3}{n-1}$

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

$T_{n} = T_3$

Hence,

$T_{2020} = T_3$

Calculating $T_3$

$T_{3} = \frac{10 + 20}{2}$

$T_{3} = \frac{30}{2}$

$T_{3} = 15$

Recall that $T_{2020} = T_3$

$T_{2020} = 15$

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