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I'm studying for a test, and I am having a hard time with this particular exercise.

The first member is equal to 7 and the fifth member is equal to 59. How many members should be taken in to the sequence that it would amount to 24,217?

So far I have found out that d=13, but having trouble with the equation.

Any help would be appreciated. Thank you.

1 Answers 1

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If the first number in an arithmetic progression is $a$ and the increment is $d$, term $i$ is $a+(i-1)d\ \ $. So the sum of $n$ terms is $\sum_{i=1}^n a+(i-1)d=na+n(n-1)d/2\ \ $. In your case, $a=7, d=(59-7)/4=13\ \ \ $, so you can just solve the quadratic equation $7n+13(n-1)n/2=24217\ \ $.

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    Thank you! This is what I got "13n2 - 6n - 48434 = 0". Is this correct? I can't seem to solve it.2011-08-24
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    @BeatShot: It should be $+n$, as you get $+2\cdot 7$ from the first term and $-13$ from the second (after multiplying by $2$ to clear the denominator)2011-08-24
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    I still dont't manage to solve it. Could you please go a little futher from the quadratic equation part?2011-08-24
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    Finally solved it! The answer is 61. Thank you very much for your help.2011-08-24
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    Two different ways:(i) Do you know the Quadratic Formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$? (ii) Note that $n$ will be much smaller than $n^2$. So $n^2+n\approx n^2$. Find $y$ such that $13y^2=48434$ (calculator). Your $n$ will be near $y$, a little smaller. You'll find it soon.2011-08-24
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    Thank you for replying Andre. I know the Quadratic Formula, and I solved it. There was a small (stupid) mistake in the discriminant part.2011-08-24