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Consider the arithmetic sequence 5,7,9,11, …. Derive a formula for (i) the nth term and (ii) the sum to n terms. (iii) Hence find the sum of the first 20 terms.

We can easily identify the first term (5) The common difference can be found by subtracting the n th term from the (n+1) th term 7-5=9-7=11-9=2 Therefore: U 1 =5 and d=2 The IB formula booklet provides the g...
JN
Answered by Jan Niklas F. • Maths tutor
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Differentiate y=(3x-1)/(2x-1)

First, recognise that the function is a fraction and recall the quotient rule. y=u/v dy/dx=(vu'-uv')/v 2 , where u' and v' is the derivative of u and v respectively. Then, apply the rule. u=3x-1, v=2x-1 u'=3...
MM
Answered by Martin M. • Maths tutor
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Rationalise the following: { 5 } / { 3 - sqrt(2) }

The aim here is to turn the fraction so that the denominator does not have a surd. Given that we know that any surd squared is equal to the number itself, i.e sqrt(2) * sqrt(2) equas 2, or sqrt(x) * sqrt(x) ...
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Answered by Amin S. • Maths tutor
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Solve the equation: x^2 + 9x + 20 = 0

This is a quadratic equation. There are different ways to solve quadratic equations including factorising them and using the quadratic formula. This is a simple equation so it cn be solved by factorising. It...
FM
Answered by Francesca M. • Maths tutor
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What is 3/5 of 65.

Break this question into 2. Divide 65 by 5 = 13 13 x 3 = 39
AA
Answered by Alice A. • Maths tutor
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