
Dear Q and Q,
My name is David, I'm a math club student in the sixth grade. I have been searching everywhere for the formula to mathamatical progression.
Thank you for your time,
David
Hi David,
I think you are looking for an arithmetic progression. An arithmetic progression is a sequence in which the difference between one term and the next is always the same number, called the common difference. For example
2, 5, 8, 11, ...
is an arithmetic progression since the difference between and two successive numbers is 3, the common difference. Also
1, ^{1}/_{2}, 2, ^{3}/_{2}, 3, ^{5}/_{2},...
is an arithmetic progression with a common difference of ^{1}/_{2}.
1, 4, 9, 16, 25, ...
is not an arithmetic progression.
The formula you are looking for is probably the formula that gives the sum of an arithmetic progression. This is a place where you don't need a formula, you just need to remember how to do it. For example to find the sum of the terms
2, 5, 8, 11, ..., 29, 32, 35, 38
write the sum twice, once from slallest o largeat and then from largest to smallest
sum = 2 + 5 + 8 + 11 + ... + 29 + 32 + 35 + 38
sum = 38 + 35 + 32 + 29 + ... + 11 + 8 + 5 + 2
Now add DOWN
2 x sum = 40 + 40 + 40 + 40 + ... + 40 + 40 + 40 + 40 = 13 x 40
Hence
sum = 13 x 20 = 260
Penny
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