# Thread: Sum of the arithmetic series

1. ## Sum of the arithmetic series

The first term of an arithmetic series is a and the common different is d.If the sum of the first three term of this series is 15 and the product of the first two terms is 10,find the values of a and d.Hence, calculate the sum of the first eight terms of the series.

2. ## Re: Sum of the arithmetic series

The nth term of an arithmetic sequence is given by $\displaystyle u_n = a + (n-1)d$ and the sum of n terms is given by $\displaystyle S_n = \dfrac{n}{2} (2a+(n-1)d)$

Hence the sum of three terms is $\displaystyle S_3 = \dfrac{3}{2}(2a+2d) = 3(a+d) = 15$

The product of the first two terms is $\displaystyle a \times (a+d) = 10$

You can then solve the equations simultaneously to find a and d

3. ## Re: Sum of the arithmetic series

$\displaystyle a+(a+d)+(a+2d)=3a+3d=3(a+d)=15\Rightarrow\ a+d=5$
$\displaystyle a(a+d)=10$