# Answer to Question #21891 in Calculus for Kevin

Question #21891

Hello, this is my math question relating to number sequences. Is there a specific equation for a number plus(+) every whole number less than it down to 1? [Ex.] 365+364+363+...1=?

Expert's answer

A sequence such as 1, 2, ... 365 or 365, 364, .. 1 which has aconstant difference between terms called arithmetic progression. The first

term is a1, the common difference is d, and the number of terms is n.

an = a1 + (n – 1)d

the sum of an arithmeticprogression is equal to

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

or

Sn = n/2 * (2*a1+d(n-1))

S(365)=365/2*(1+365)= 66795

term is a1, the common difference is d, and the number of terms is n.

an = a1 + (n – 1)d

the sum of an arithmeticprogression is equal to

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

or

Sn = n/2 * (2*a1+d(n-1))

S(365)=365/2*(1+365)= 66795

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