Sally is having a party. The first time the doorbell rings, one guest enters. If on each successive ring a group enters that has two more persons than the group that entered on the previous ring, how many guests will have arrived after the 20th ring?

Question

Vocaloid · Answer

it seems like they want the total # of guests at ring 20 + the ones who have already arrived at the previous rings

the pattern of guests can be describes as a series with a1 = 1 (since there's only one guest) and common difference d = 2 (since the guests are increasing by 2 each time)

n = the number of terms, or in this case, the number of rings, which is 20

first, we will have to find how many guests arrived on ring 20 using

an = a1 + (n-1)d

then, use the sum formula

sum = (n/2)(a1+an)

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