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Find the sum of the first 41 terms of the following series, to the nearest integer 11,19,27

1 Answer

6 votes

Input data

11, 19, 27

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which an = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a1.

Procedure

d = 19 - 11 = 8

d = 27 - 19 = 8

a1 = 11


a_n=11+8(n-1)

for n = 41

To find the sum of the first n terms of an arithmetic series use the formula, n terms of an arithmetic sequence use the formula,


\begin{gathered} S_n=(n(a_1+a_n))/(2) \\ \end{gathered}

a41 = 11+8(41-1)

a41 = 11+8*40

a1 = 331


\begin{gathered} S_(41)=(41(11+331))/(2) \\ S_(41)=(41(342))/(2) \\ S_(41)=6642 \end{gathered}

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