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The first three terms of an arithmetic series are p, 5p – 8, and 3p + 8 respectively. (a) Show that p=4 (b) Find the value of the 50th term in the series.

(a) If the sequence = p , 5p-8 and 3p+8 is an arithmetic sequence then the difference between successive terms must be constant.e.g. (5p-8)-(p) = (3p+8)-(5p-8)=> 4p-8 = -2p+16 => 6p = 24 => p=24/...

Answered by Daniel S. • Maths tutor

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An arithmetic progression has a tenth term (a10) = 11.1 and a fiftieth term (a50) = 7.1 Find the first term (a) and the common difference (d). Also find the sum of the first fifty terms (Sn50) of the progression.

We start off by constructing simultaneous equations as there are two variables - a and d - that we do not know. We use the formula:a_n = a + (n-1)di) 11.1 = a + 9dii) 7.1 = a + 49d
i) - ii)...

Answered by • Maths tutor

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Solve the following simultaneous equations to give a value for both x and y: 3x+3y=9 and 2x+3y=5

Subtract the bottom equation from the top equation to get 3x-2x=9-5 (you don't see no y values in this equation as the y's have disappeared and cancelled eachother out as 3y-3y=0)2) So 3x-2x=9-5 equ...

Answered by Amy F. • Maths tutor

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simplify fully: (3x^2 - 8x -3)/(2x^2 -6x)

First of all, to simplify this fraction, we need to factorise the top and bottom equations. We shall start with the top equation. Now looking at the equation: 3x² - 8x -3, we know that it's a q...

Answered by Amanda H. • Maths tutor

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Prove that the product of 3 consecutive integers is divisible by 6

If you set the three consecutive integers to be n, n+1 and n+2, we know that one of the numbers must be divisible by 2 and one must be divisible by 3. For example if you had your three numbers as: 5, 6, 7...

Answered by Shreeya K. • Maths tutor

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