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25 votes
25 votes
Find the sum of the sequence.
47 +48 +49 +50+...+116

User Feralvam
by
3.1k points

1 Answer

18 votes
18 votes

Answer:

5705

Explanation:

The sum of an arithmetic series is the product of the number of terms and the average term. The average term is the average of the first and last terms.

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Here, the first term is 47, the last term is 116, and the number of terms is (116 -46) = 70. The common difference is 1. (The terms are consecutive integers.)

The sum is ...

sum = (70)(47 +116)/2 = 35(163) = 5705

The sum of the sequence is 5705.

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Alternate solution

The sum of n consecutive natural numbers is n(n+1)/2. The sum of the numbers 47 to 116 will be the sum of the first 116 natural numbers less the sum of the first 46.

sum = (116)(117)//2 -(46)(47)/2 = 6786 -1081 = 5705

User Zeacuss
by
2.9k points