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Aleks04 [339]
4 years ago
9

YEAR 9 MATHS- SEQUENCES

Mathematics
1 answer:
Triss [41]4 years ago
7 0

Answer:

see below

Step-by-step explanation:

This is an arithmetic sequence. The explicit formula for an arithmetic sequence is aₙ = a₁ + (n - 1)d where a₁ is the first term and d is the common difference. In this case a₁ = 9 and d = 6 so we have:

aₙ = 9 + (n - 1) * 6

aₙ = 9 + 6n - 6

aₙ 6n + 3

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<h2>Explanation:</h2><h2></h2>

Here we need to set a system of two linear equations in two variables. So:

  • <em>The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:</em>

Let x \ and \ y be those digits, then:

x+y=8 \ \ldots eq1

  • <em>If 9 is added to a number then both the digits become equal. find the number:</em>

<em />

<em />10x+y+9 \ldots expression \ 1<em />

<em />

But from eq 1:

y=8-x

Substituting y into the expression 1:

10x+(8-x)+9=9x+17

The x-value will be found by hit and trial, so:

  • Let x = 1:

9x + 17 = 9(1)+17 = 26

We have to reject this solution because digits are different.

  • Let x = 2:

9x + 17 = 9(2)+17 = 35

We have to reject this solution because digits are different.

  • Let x = 3:

9x + 17 = 9(3)+17 = 44

<em>Then this is a two digit number formed by two equal digits. </em>

Finally, the number is:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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