document.write( "Question 1070586: Three numbers form an arithmetic sequence. The first term minus the third term is 8. When the 1st, 2nd, and 3rd terms are increased by 3, 5, and 8 respectively, the resulting numbers forms a geometric sequence. Find the common difference of the arithmetic sequence, find the first four terms of the geometric sequence, and the common ratio of the geometric sequence. \n" ); document.write( "
Algebra.Com's Answer #685656 by htmentor(1343)\"\" \"About 
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The nth term of an arithmetic series can be written a_n = a + (n-1)d where
\n" ); document.write( "a is the 1st term and d is the common difference
\n" ); document.write( "Given that the 1st term minus the 3rd term is 8, we have
\n" ); document.write( "a - (a + 2d) = 8 -> -2d = 8, or d = -4
\n" ); document.write( "So a_n = a - 4(n-1)
\n" ); document.write( "Adding 3, 5 and 8 to the 1st three terms gives g_1 = a + 3, g_2 = a + 1, and g_3 = a
\n" ); document.write( "Since the ratio of successive terms of a geometric sequence is a constant, r, we can write:
\n" ); document.write( "r = (a+1)/(a+3) = a/(a+1)
\n" ); document.write( "Solve for a:
\n" ); document.write( "a^2 + 2a + 1 = a^2 + 3a -> a = 1
\n" ); document.write( "The arithmetic sequence is a_n = 1 - 4(n-1)
\n" ); document.write( "The common ratio is 1/(1+1) = 1/2
\n" ); document.write( "So the 1st 4 terms of the geometric sequence are 4, 2, 1, 1/2\r
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