document.write( "Question 1176312: In a geometric progression the 5th term is 9 times the 3rd term and the sum of the 6th and 7th terms is 1944. Determine (a) the common ratio,(b) the 1st term
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Algebra.Com's Answer #803181 by htmentor(1343) $\"\"$ $\"About$

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The nth term of a G.P. is a_n = a*r^(n-1), where a is the 1st term and r is the
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\n" ); document.write( "Since a_5 = 9*a_3, we have ar^4 = 9ar^2 -> r^2 = 9
\n" ); document.write( "There are two possibilities: r = 3, or r = -3
\n" ); document.write( "If r = 3, a_6 + a_7 = 1944 = a(3)^5 + a(3)^6 -> a = 1944/((3)^5 + (3)^6)) = 2
\n" ); document.write( "If r = -3, a = 1944/((-3)^5 + (-3)^6) = 4
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