Find the sum of the AP 1,2,7,10,13,16,...,1000. answer= 167167 (i can solve this)
Every 3rd term in the AP is taken out, that is 7,16,... Find the sum of the remainder terms.
How to solve the part 2? answer is 111445.
Can you show me the working? thanks
Every 3rd term in the AP is taken out, that is 7,16,... Find the sum of the remainder terms.
How to solve the part 2? answer is 111445.
Can you show me the working? thanks
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Supposing the arithmetic progression is actually: 1, 4, 7, 10, 13, 16, ... , 1000.
Add 2 to every term: 3, 6, 9, ..., 1002
The number of terms in this progression is 1002 / 3 = 334
The sum of the terms (following the method of Gauss) is: (1000 + 1) (334/2) = 167167
The numbers being taken out are: 7, 16, 25, 34, ...,
Add 2 to every term: 9, 18, 27, 36,...,
The last term must be 1002 or less.
1002 / 9 = 111 + (1/3)
111 (9) = 999
999 - 2 = 997 <- this is the last term in the series beginning 7, 16, 25,...
The number of terms in this series is 999 / 9 = 111.
The sum of 7 + 16 + 25 + ... + 997 = (7 + 997) (111/2) = 55722
167167 - 55722 = 111445
Add 2 to every term: 3, 6, 9, ..., 1002
The number of terms in this progression is 1002 / 3 = 334
The sum of the terms (following the method of Gauss) is: (1000 + 1) (334/2) = 167167
The numbers being taken out are: 7, 16, 25, 34, ...,
Add 2 to every term: 9, 18, 27, 36,...,
The last term must be 1002 or less.
1002 / 9 = 111 + (1/3)
111 (9) = 999
999 - 2 = 997 <- this is the last term in the series beginning 7, 16, 25,...
The number of terms in this series is 999 / 9 = 111.
The sum of 7 + 16 + 25 + ... + 997 = (7 + 997) (111/2) = 55722
167167 - 55722 = 111445