document.write( "Question 1140428: the first term of a geometric series is 3,the last term is 768 if the sum of the term is 1533 find the common ratio and the number of terms \n" ); document.write( "
Algebra.Com's Answer #760963 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "The formula for the sum of the first \"n\" terms of any geometric progression\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"S%5Bn%5D\" = \"%28a%5B1%5D%2Aq%5En-a%5B1%5D%29%2F%28q-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(where \"q\" is the common ratio) can be written in an equivalent form \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"S%5Bn%5D\" = \"%28a%5Bn%5D%2Aq+-+a%5B1%5D%29%2F%28q-1%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, with the given data,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    1533 = \"%28768%2Aq-3%29%2F%28q-1%29\",\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "or, simplifying\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    768*q - 3 = 1533*(q-1)\r\n" );
document.write( "\r\n" );
document.write( "    768q - 3 = 1533q - 1533\r\n" );
document.write( "\r\n" );
document.write( "    1533 - 3 = 1533q - 768q\r\n" );
document.write( "\r\n" );
document.write( "    1530 = 765q\r\n" );
document.write( "\r\n" );
document.write( "    q = \"1530%2F765\" = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the common ratio is just found: it is 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next,  to find \"n\", the number of terms, use the general formula for the n-th term\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    768 = \"3%2A2%5E%28n-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "    \"2%5E%28n-1%29\" = \"768%2F3\" = 256\r\n" );
document.write( "\r\n" );
document.write( "    ============>  n - 1 = 8;  hence,  n = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The number of terms is 9 and the common ratio is 2.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "--------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On geometric progressions,  see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for geometric progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Geometric progressions\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );