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A sequence increases by 5 each time and the first term is x. The sum of the first four terms is 54. Set up and solve an equation to work out the value of x.

The first term is x, and if it increases by 5 each time then the second term is x+5, third is x+10, and the fourth is x+15. Adding these values together we get 4x+5+10+15, and this equals 54. Therefore; 4x+3...
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Answered by Tom P. • Maths tutor
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The work in an office takes 200 hours to complete every week. Each person in the office works 35 hours a week. What is the smallest number of people needed to complete the work?

To answer this question we need to divide the hours needed to complete work (200) by how much a person works a week (35). The key aspect of this question that catches people out is that when dividing 200 by ...
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Answered by Tom P. • Maths tutor
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The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Note here: u_n indicates u subscript n. (a) u_1 = 48 and the ratio, r = 0.6 Using a calculator, u_2 = 48 x 0.6 = 28.8 u_3 = 28.8 x 0.6 = 17.28 (b) We have the known result that the sum to infinity of a geome...
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Answered by Felix S. • Maths tutor
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Express 0.545454... as a fraction in its simplest form.

First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x. 100x = 54.54545454... But, the decimal part of this number is what we...
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Answered by Felix S. • Maths tutor
32171 Views

Solve x^2-5*x+6=0

There are 2 methods we can use here. Method 1 - Factorisation If we can rewrite the equation so that it looks like (x+a)*(x+b)=0, where 'a' and 'b' are numbers, then we can easily find a solution. If one or ...
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Answered by Hannah D. • Maths tutor
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