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.
answer is 1125 beads but provide the way to get this answer
The series given can be written in summation notation as $\sum_{n=1}^{18} (3 + 7(n-1))$.
The lower limit of the sum is 1 and the upper limit is 18.
The explicit formula for the sum is $\frac{n}{2}[2a + (n-1)d]$, where $n$ is the number of terms, $a$ is the first term, and $d$ is the common difference. In this case, $n=18$, $a=3$, and $d=7$.
Plugging in the values, we get $\frac{18}{2}[2(3) + (18-1)(7)] = 1125$.
To find the total number of beads in the necklace, we need to sum up all the beads in each row. This can be done by calculating the sum of the series using the explicit formula.