A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.��Sn: 2 + 5 + 8 + . . . + ( 3n - 1) = n(1 + 3n)/2

Question

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Answer 1

Which answer describes the calculations that could be used to solve this problem?

Bonita brought 3 bags of apples and 2 pounds of grapes to the picnic. Each bag of apples weighed 4 pounds. How many pounds of apples and grapes did Bonita bring to the picnic?

Answer 2

you know that summing from 1 to n:

sum(1) = n
sum(n) = n(n+1)/2

so, sum(3n-1) = 3sum(n)-sim(1)
= 3n(n+1)/2 - n
= (3n^2+3n-2n)/2
= (3n^2+n)/2
= n(3n+1)/2