Question

Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3 + 10 + 17 + 24 + ...

a. Use summation notation to write the series. Explain what the numbers in the summation notation represent in this situation and how you found the expression used in the summation.
b. Find the total number of beads in the necklace. Explain your method for finding the total number of beads.

Answer 1

A) \[\large \sum_{n=1}^{18} (3 + (n - 1)7)\]

I don't know how to do B tho. Can anyone help me?

Answer 2

sum(3+(n-1)7)=sum(7n-4)=sum(7n)-sum(4)=7sum(n)-sum(4) from n=1 to n=18

Answer 3

how does sum(3+(n-1)7) = sum(7n-4) ?

Answer 4

3+(n-1)7 = 3+7(n-1) = 3+(7n-7) = 7n+(3-7) = 7n-4

Answer 5

also sum(4) from n=1 to n=18 is just 4*18; finding sum(n) from n=1 to n=18 shouldn't be too difficult

Answer 6

I see thanks :)

Answer 7

:) also http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html might help to find sum(n)