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3 years ago

A teacher's age is 6 years greater than 2 times a student's age. A principal's age is 10 years greater than 3 times

Mathematics

1 answer:

dlinn [17]3 years ago

5 0

Answer:

b. <u>x + 4</u>

Solution:

Student's age = x

Teacher's age = 6 + 2x

Principal's age = 10 + 3x

Difference in the age of the teacher and principal

(10 + 3x) - (6 + 2x)

= 10 + 3x - 6 - 2x

= (10 - 6) + (3x - 2x)

= 4 + x

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block 1 - 1, 2 - length 2

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block 3 - 1, 2, 2, 2 - length 4

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Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

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In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

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So, the sum of the first 1234 terms in the sequence is 2419.

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2 years ago