Sum of the arithmetic series

**faraday** · July 6th 2011, 05:05 AM

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.

**e^(i*pi)** · July 6th 2011, 05:12 AM

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

**Archie Meade** · July 6th 2011, 05:40 AM

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).

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