# Sum of the arithmetic series

• Jul 6th 2011, 05:05 AM
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.
• Jul 6th 2011, 05:12 AM
e^(i*pi)
Re: Sum of the arithmetic series
The nth term of an arithmetic sequence is given by $u_n = a + (n-1)d$ and the sum of n terms is given by $S_n = \dfrac{n}{2} (2a+(n-1)d)$

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

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

You can then solve the equations simultaneously to find a and d
• Jul 6th 2011, 05:40 AM
$a+(a+d)+(a+2d)=3a+3d=3(a+d)=15\Rightarrow\ a+d=5$
$a(a+d)=10$