Mathematics for Science Streams

Solutions for Dailly challenge 01/01/2022. Continue reading for explanations.
Grade 10:

1st step: Let x = 5.4`3`2`
x = 5.432432432...
2nd step: Multiply both sides by 1000. Why? Because we have 3 recurring digits aftet the coma. (4`3`2`) 3 digits > 1000 (3 zeros).
Then we have:
1000x = 5432.432432432...
3rd step: Subtract the first equation from the second equation:

1000x — x = 5432.432432432... — 5.432432432...

We remain with :

999x = 5427 then solve for x...................

Grade 11
1st step:
Expand the bases on the numerator. Why? Because we have addition of exponents and we know that they are as a result of same bases multiplying.
2nd step:
Factor out the common factor 3ⁿ. Then simplify..................

Grade 12:
1st step:

You know that it's a quadratic sequence (given).
You know that the general n-th term of a quadratic sequence is given by: Tn = an² + bn + c
Where:
2a = second difference (common)
3a + b = first term of the first difference
a + b + c = first term of the sequence
2nd step:
Solve for a, b and c to find the Tn of the sequence.
3rd step:
Substitute n = 26 to find the 26th term of the sequence.
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