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The first four terms of an arithmetic sequence are : 11, 17, 23, 29. In terms of n, find an expression for the nth term of this sequence.

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. We can work this out for the sequence 11, 17, 23, 29. To go from the 1st term (11) to the 2...
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Answered by Aman G. • Maths tutor
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Write x^2 + 8x + 7 in the form (x + a)^2 + b

We work from right to left (x + a) 2 = x 2 + 2ax + a 2 2a = 8 [coefficients of x must match] a = 4 (x + 4) 2 = x 2 + 8x + 16 [substitute in a = 4] x 2 + 8x + 16 + b = x 2 + 8x + 7 [equate sides and solve for...
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Answered by Will M. • Maths tutor
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What is £23 increased by 4%?

There are two steps to solving this problem. First, we want to find out how much the increase itself is, so we want to calculate 4% of £23. Then, we want to add the result to the £23. That will give us the f...
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Answered by Giulia B. • Maths tutor
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Solve for x and y, with x and y satisfying the equations x+4y=5 and 2x+2y=16.

x=9 y=-1
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Answered by Lucy S. • Maths tutor
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Solve the simultaneous equations for x and y: 2x+4y=-12 and y=-x-2

From the question we have y = -x - 2 so we can sub in -x-2 everywhere there is a y in the first equation. The equation is then 2x+4(-x-2) = -12 expanding the brackets we get -2x-8=-12 which you can then rear...
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Answered by Daniel G. • Maths tutor
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