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 + ...
If you were to write this series in summation notation,
give the lower limit of the sum
the upper limit of the sum
the explicit formula of the sum
Find the total number of beads in the necklace. Explain your method for finding the total number of beads.
this is what I have so far
1(first term)
18(last term)
3 + (n-1)*7 = 7n - 4
To find the total number of beads in the necklace, you would need to add up the number of beads in each row according to the given series. Since the number of beads per row is given by the series 3 + 10 + 17 + 24 + ..., we can see that this is an arithmetic series with a first term of 3, a common difference of 7, and a total of 18 terms.
To find the total number of beads, we can use the formula for the sum of an arithmetic series:
S = (n/2)(a + l)
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
Plugging in the values:
n = 18 (since there are 18 rows)
a = 3 (first term)
l = 7(18) - 4 = 126 - 4 = 122 (last term)
S = (18/2)(3 + 122)
S = 9(125)
S = 1125
Therefore, the total number of beads in the necklace is 1125.