SOLUTION: 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

SOLUTION: 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_

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?
Answer by greenestamps(13334) (Show Source): You can put this solution on YOUR website!

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.

The number of terms is 40; the average of the terms is the average of the first and last:

The sum of the terms in S_p is then

The sum S_1+S_2+...+S_10 is then

ANSWER: 80200

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