document.write( "Question 978886: The first,fifth and seventh term of an Arthimetic Progression(A.P) are equal to the first three consecutive terms of a decreasing Geometric Progression(G.P). The first term of each progression is 56, the common difference of the A.P IS d and the common ratio of the G.P is r
\n" ); document.write( "a)(i)Write two equations involving d and r
\n" ); document.write( " (ii)Find the values of d and r
\n" ); document.write( "(b) find the sum of the first 10 terms of:
\n" ); document.write( " (I) The arithmetic progression
\n" ); document.write( " (ii) The geometric progression \n" ); document.write( "
Algebra.Com's Answer #600229 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "You will need these formulas:\r\n" );
document.write( "\r\n" );
document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\" <--nth term of an A.P.\r\n" );
document.write( "\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\" <--nth term of an G.P.\r\n" );
document.write( "

\n" ); document.write( "The first,fifth and seventh term of an Arthimetic Progression(A.P)...
\n" ); document.write( "The first term...is 56, the common difference of the A.P IS d
\n" ); document.write( "
\r\n" );
document.write( "first term of A.P. = \"a%5B1%5D\" = 56\r\n" );
document.write( "fifth term of A.P. = \"a%5B5%5D=a%5B1%5D%2B%285-1%29d=56%2B4d\"\r\n" );
document.write( "seventh term of A.P. = \"a%5B7%5D=a%5B1%5D%2B%287-1%29d=56%2B6d\"\r\n" );
document.write( "

\n" ); document.write( "...the first three consecutive terms of a decreasing Geometric Progression(G.P).
\n" ); document.write( "The first term...is 56,...
\n" ); document.write( "and the common ratio of the G.P is r
\n" ); document.write( "
\r\n" );
document.write( "first term of G.P. = \"a%5B1%5D\" = 56\r\n" );
document.write( "second term of G.P. = \"a%5B2%5D=a%5B1%5Dr%5E%282-1%29d=56r%5E1=56r\"\r\n" );
document.write( "third term of G.P. = \"a%5B3%5D=a%5B1%5Dr%5E%283-1%29d=56r%5E2\"\r\n" );
document.write( "

\n" ); document.write( "a)(i)Write two equations involving d and r\r
\n" ); document.write( "\n" ); document.write( "The first,fifth and seventh term of an Arithmetic Progression(A.P) are
\n" ); document.write( "respectively equal to the first three consecutive terms of a decreasing
\n" ); document.write( "Geometric Progression(G.P).
\n" ); document.write( "
\r\n" );
document.write( "\"system%2856%2B4d=56r%2C56%2B6d=56r%5E2%29\"\r\n" );
document.write( "

\n" ); document.write( "(ii)Find the values of d and r
\n" ); document.write( "
\r\n" );
document.write( "Divide the first equation through by 4 and the second through by 2\r\n" );
document.write( "\"system%2814%2Bd=14r%2C28%2B3d=28r%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for d  \"d=14r-14\"\r\n" );
document.write( "Substitute it in the second equation:\r\n" );
document.write( "\r\n" );
document.write( "\"28%2B3d=28r%5E2%29\"\r\n" );
document.write( "\"28%2B3%2814r-14%29=28r%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve that quadratic for r.  [You will get two solutions for r, ignore r=1,\r\n" );
document.write( "because to have a decreasing G.P., r must be a fraction less than 1.\r\n" );
document.write( "\r\n" );
document.write( "Substitute to find d\r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "(b) find the sum of the first 10 terms of:
\n" ); document.write( " (I) The arithmetic progression
\n" ); document.write( " (ii) The geometric progression
\n" ); document.write( "
\r\n" );
document.write( "You will need these formulas:\r\n" );
document.write( "\r\n" );
document.write( "\"S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29\" <--sum of first n terms of an A.P.\r\n" );
document.write( "\"S%5Bn%5D=a%5B1%5D%281-r%5En%29%2F%281-r%29\" <--sum of first n terms of a G.P.\r\n" );
document.write( "\r\n" );
document.write( "Now you can do the problem.  \r\n" );
document.write( "\r\n" );
document.write( "If you get stuck, tell me in the thank-you\r\n" );
document.write( "note form below, and I'll get back to you by email.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );