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Could someone please explain how they get to an answer? Thanks!

 Dec 3, 2020
 #1
avatar+114526 
+2

 

Note that

101^2  -97^2 =  792

93^2  - 89^2  = 728

85^2  - 81^2  = 664

77^2 - 73^2  =  600

.....

13^2 - 9^2   = 88

5^2 - 1^2  =   24

 

Writing this in reverse, we  have  the series   24+ 88 +........ +.600 + 664 + 728 + 792

 

This is the  sum of an arithmetic  series

 

Sum =  (n/2)  [ 2a  + (n -1)  d  ] 

 

a = first term 

n = number of  terms which  is figured  as    (101 - 5) / 8  + 1 =      96/8  + 1  =  12 + 1   = 13

d = common difference  between  terms =  64

 

 

So....the sum  is

 

(13/2) [ 2(24) +  (12) (64 ) ]  =   5304

 

 

cool cool cool

 Dec 3, 2020
edited by CPhill  Dec 3, 2020
 #2
avatar+27 
0

Thank you so much! By any chance can you help me out with the part b too? thanks!

 Dec 3, 2020
 #4
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0

See detailed solution for # 2 here:  https://web2.0calc.com/questions/please-help-question-not-answered#r2

Guest Dec 4, 2020
 #3
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0

Part (b) works out to (a + (2n + 1)d)^2 - (a + (2n)d)^2 + ... + (a + d)^2 - a^2 = (a + (2n + 1) d + (a + 2nd + ... + a + d) + a = n(3a + (n + 2)d).

 Dec 4, 2020

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