So I got this question in my exam yesterday, and only a few people from my school could solve this.
What's so hard about it? I have learned the simple arithmetic questions, but I don't really understand how to do this one.
formulas:
In the arithmetic the tenth organ is 4 times bigger than the third organ.
The amount of all first 50 organs is 3725. Find A1 and D (the first and the difference of the series).
How do I solve it?
You write the equations for the 10th term, and 3rd term:
$T_n = a + (n-1)d$
$T_3 = a + (3-1)d = a + 2d$
$T_{10} = a + (10-1)d = a + 9d$
You are told that $T_{10}$ is 4 times $T_3$, or that: $T_{10} = 4T_{3}$
Which means:
$a + 9d = 4(a + 2d)$
And lastly, the sum all the first 50 terms is 3725, which means:
$S_n = \dfrac{n(2a+(n-1)d)}{2}$
$S_{50} = \dfrac{50(2a+(50-1)d)}{2} = 3725$
You should be able to solve those.