# Progressions

• Feb 29th 2008, 11:08 AM
bjhopper
Progressions
the sum of three consecutive terms of an arithmetic progression is 21.if these numbers are increased by 1,3, and 10 respectively, the resulting numbers form consecutive terms of a geometric proression. Find the numbers

bj
• Feb 29th 2008, 01:12 PM
Plato
Quote:

Originally Posted by bjhopper
the sum of three consecutive terms of an arithmetic progression is 21.if these numbers are increased by 1,3, and 10 respectively, the resulting numbers form consecutive terms of a geometric proression. Find the number

bjhopper, can you solve this system?
$\begin{array}{l}
a + \left( {a + d} \right) + \left( {a + 2d} \right) = 21 \\
\frac{{a + 1}}{{a + d + 3}} = \frac{{a + d + 3}}{{a + 2d + 10}} \\
\end{array}
$