#### homeschool girl

##### Junior Member

- Joined
- Feb 6, 2020

- Messages
- 62

part (a) Compute the sum \(\displaystyle 101^2 - 97^2 + 93^2 - 89^2 + \cdots + 5^2 - 1^2.\)

part (b) Compute the sum \(\displaystyle (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)

I know I need to pair the terms together and apply difference of squares, but don't know which terms I should pair and what to do after. I would very much appreciate some help. thanks!

part (b) Compute the sum \(\displaystyle (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + \cdots + (a+d)^2 - a^2.\)

I know I need to pair the terms together and apply difference of squares, but don't know which terms I should pair and what to do after. I would very much appreciate some help. thanks!

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