# Sum of the arithmetic series

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• July 6th 2011, 05:05 AM
faraday
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.
• July 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
• July 6th 2011, 05:40 AM
Archie Meade
Re: Sum of the arithmetic series
Quote:

Originally Posted by faraday
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.

Alternatively, working with the arithmetic pattern..

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

$a(a+d)=10$

into which you may substitute the value obtained for (a+d).