document.write( "Question 1108530: 6250 + 1250 + 250 + ... +2 \n" ); document.write( "
Algebra.Com's Answer #723590 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
we have a geometric series
\n" ); document.write( ":
\n" ); document.write( "x(n) = ar^(n-1) with a=6250 and r=(1/5)
\n" ); document.write( ":
\n" ); document.write( "2 = 6250(1/5)^(n-1)
\n" ); document.write( ":
\n" ); document.write( "(2/6250) = (1/5)^(n-1)
\n" ); document.write( ":
\n" ); document.write( "(1/3125) = (1/5)^(n-1)
\n" ); document.write( ":
\n" ); document.write( "n-1 = log (base 1/5) (1/3125)
\n" ); document.write( ":
\n" ); document.write( "n-1 = 5
\n" ); document.write( ":
\n" ); document.write( "n = 6
\n" ); document.write( ":
\n" ); document.write( "there are 6 terms to sum
\n" ); document.write( ":
\n" ); document.write( "Note 2 = 6250(1/5)^5 = 6250/3125 = 2
\n" ); document.write( ":
\n" ); document.write( "the sum of the first n terms in a geometric sequence is
\n" ); document.write( ":
\n" ); document.write( "S(n) = a(1 - r^n) / (1 - r)
\n" ); document.write( ":
\n" ); document.write( "for this problem n = 6 and r = 1/5
\n" ); document.write( ":
\n" ); document.write( "S(6) = 6250(1 - (1/5)^6) / (1 - (1/5))
\n" ); document.write( ":
\n" ); document.write( "S(6) = 6250(1 - 0.000064) / (1 - (1/5))
\n" ); document.write( ":
\n" ); document.write( "*****************************
\n" ); document.write( "S(6) = 6250 * 1.24992 = 7812
\n" ); document.write( "*****************************
\n" ); document.write( ":
\n" ); document.write( ": \n" ); document.write( "
\n" );