document.write( "Question 1199272: Partial Sum of a Geometric Sequence Find the sum of the first ten terms of the sequence
\n" ); document.write( "a + b, a^2 + 2b, a^3 + 3b, a^4 + 4b,... \n" ); document.write( "
Algebra.Com's Answer #833068 by ikleyn(52788)\"\" \"About 
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\n" ); document.write( "Partial Sum of a Geometric Sequence Find the sum of the first ten terms of the sequence
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document.write( "Split your partial sum into the sum of two sequances.\r\n" );
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document.write( "One sequence is a geometric progression\r\n" );
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document.write( "    a,  a^2,  a^3,  a^4,  . . . ,  a^10.    (1)\r\n" );
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document.write( "The other sequence is an arithmetic progression\r\n" );
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document.write( "    b,  2b,  3b,  4b,  . . . ,  10b.        (2)\r\n" );
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document.write( "Then apply standard formulas to each sequence separately.\r\n" );
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document.write( "As the last step, combine two formulas together.\r\n" );
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document.write( "ANSWER.  The sum is  S = \"%28a%5E11-a%29%2F%28a-1%29\" + 55b.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic and geometric progressions see\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
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\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
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\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
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topics
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\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
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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