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.
The series 3 + 10 + 17 + 24 + ... can be written in summation notation as:
∑ (7n - 4), from n=1 to n=18
Lower limit of the sum: n = 1
Upper limit of the sum: n = 18
Explicit formula of the sum: ∑ (7n - 4), from n=1 to n=18
To find the total number of beads in the necklace, we need to find the sum of the series. This can be done by substituting the upper and lower limits into the explicit formula and calculating the sum:
∑ (7n - 4) = (7(1) - 4) + (7(2) - 4) + ... + (7(18) - 4)
= 3 + 10 + 17 + ... + 121
= 1128
Therefore, there are a total of 1128 beads in Dante's necklace.