How To Find The Sum of an Arithmetic Series - Algebra

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Can you help me factor 16k³+24k²+9k+1 please

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[@JustBaileey]

I haven't come across any arithmetic sum series that calculate any negative decreasing sequences. For example i need to find the sum of the first 11 term numbers in a series 3,-1,-5,-9... I found nth rule to be Un=-4n+7 which gave me the last term -37. When I apply the Sn=n(a+l)/2 i get -187 but for some odd reason, I recall that we can't have a neative sum value. I could be wrong.

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[@josephmagnotti-jz5gy]

There's 54 increments of 3 from 4 to 58,, so
54 x 3 = 162, and 4 + 162 = 166.

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[@RossVergelGaid]

Where u get the -1 in both sides in the first example where 58=3n+1 you subtract each sides by 1?

[@blazemajorofficial]

yes you have to isolate n so first subtract 1 and divide both sides by 3 then n=19

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[@shadowdiamondfight9863]

Can someone derived the Formula 1 of this?
Sn = n/2 [ 2a1 + (n-1)d]
Please 😢

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