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The partial sum of the first n terms of a geometric series whose first term is a1 and common ratio is r (not = 1) is given by:\r
\n" ); document.write( "\n" ); document.write( "Sn = a1(1-r^n)/(1-r) \r
\n" ); document.write( "\n" ); document.write( "But we need to find the common ratio, r.
\n" ); document.write( "We can get it from: an = a1r^(n-1)
\n" ); document.write( " a4 = a1r^(n-1) Substitute a1 = 4, a4 = 256, and n = 4
\n" ); document.write( " 256 = 4r^(4-1)
\n" ); document.write( " 256 = 4r^3 Divide both sides by 4.
\n" ); document.write( " 64 = r^3 Take the cube root of both sides.
\n" ); document.write( " r = 4 The common ratio. \r
\n" ); document.write( "\n" ); document.write( "In this geometric series, a1 = 4, a4 = 256, so the series looks like this:\r
\n" ); document.write( "\n" ); document.write( "4, 4^2, 4^3, 4^4, ... or 4, 16, 64, 256, ... and the common ratio, r, is 4\r
\n" ); document.write( "\n" ); document.write( "The partial sum of the first 4 terms S4, is:
\n" ); document.write( " S4 = 4(1 - 4^4)/(1-4)
\n" ); document.write( " S4 = 4(1 - 256)/(-3)
\n" ); document.write( " S4 = 4(-255)/(-3)
\n" ); document.write( " S4 = -1020/(-3)
\n" ); document.write( " S4 = 340 \n" ); document.write( "