Sum of the arithmetic series

Printable View

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).

All times are GMT -8. The time now is 12:18 AM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.