Question 1191488
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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.<br>
The number of terms is 40; the average of the terms is the average of the first and last:<br>
{{{(p+(p+39(2p-1)))/2=(80p-39)/2}}}<br>
The sum of the terms in S_p is then<br>
{{{(40)((80p-39)/2)=20(80p-39)=1600p-780}}}<br>
The sum S_1+S_2+...+S_10 is then<br>
{{{sum((1600p-780),1,10) = 1600*sum(p,1,10)-10(780)=1600(55)-7800=88000-7800=80200}}}<br>
ANSWER: 80200<br>