Mental math: .25 + .45 + .65 + .85 +....+1.45=___The answer is 5.95. What is the best way to derive this mentally?

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lfryerda eNotes educator| Certified Educator

Since each term in the sum is 0.2 higher than the term before it, we have the total sum:


for a total of 7 terms.  I find the 0.05 for each part to be annoying, so that's a total of 0.35, with the rest of the sum as 


Now, I add in groups of 1.0, so think in pairs:




with the last one getting its own group


This means when we add this up, we end up with



The total sum is 5.95