document.write( "Question 1191488: For p = 1,2,3,...,10 let S_p be the sum of the first 40 terms of the arithmetic progression whose first term is p and whose common difference is 2p-1. What is the value of S_1 + S_2 +...+ S_10? \n" ); document.write( "

Algebra.Com's Answer #823288 by greenestamps(13334) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the first 40 terms of the sequence with first term p and common difference (2p-1) is the number of terms, multiplied by the average of the terms.

\n" ); document.write( "The number of terms is 40; the average of the terms is the average of the first and last:

\n" ); document.write( " $\"%28p%2B%28p%2B39%282p-1%29%29%29%2F2=%2880p-39%29%2F2\"$

\n" ); document.write( "The sum of the terms in S_p is then

\n" ); document.write( " $\"%2840%29%28%2880p-39%29%2F2%29=20%2880p-39%29=1600p-780\"$

\n" ); document.write( "The sum S_1+S_2+...+S_10 is then

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\n" ); document.write( "ANSWER: 80200

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